[ periodic orbit theory | transitions to chaos | chaos books | quantum field theory | field theory book | group theory | in progress | miscelania ]


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Predrag Cvitanović: periodic orbit theory publications

[ chaotic field theory | turbulence | symmetries of dynamics | Kuramoto-Sivashinsky | periodic orbits extraction | noise | wave chaos | modulated amplitude waves | periodic orbits from data | kill periodic orbits | nonhyperbolic dynamics | phase transitions | deterministic diffusion | cycle expansions | quantum determinants | geometry of chaos ]

starstar Periodic orbit research overview
pdf Abstract of a general colloquium on the periodic orbit theory

Chaotic field theory

Program whose goal is a theory of turbulent dynamics of classical, stochastic and quantum fields. Chaotic field theory is developed in two directions: 1) explorations of the feasibility of describing weak turbulence in terms of spatiotemporally recurrent patterns, and 2) new perturbation theory methods for computing corrections about nontrivial saddles of path integrals.

Read the sketch paper first, perhaps click through the trace formulas seminar next.

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Predrag Cvitanović
Chaotic Field Theory: a sketch,
Physica A 288 , 61 (2000) [ nlin.CD/0001034 , NSF review panel critique ]

State space geometry of moderate Re turbulence

Getting hang of turbulence for plumbers: pipes and planes. Program manifesto, gentle multimedia introduction, a few talks.

pdf Predrag Cvitanović
You know how to cycle? That's rich
J. Fluid Mech. Focus on Fluids 722, (2013)

pdf Predrag Cvitanović and John F. Gibson
Geometry of state space in plane Couette flow
in Bruno Eckhardt, ed., Adv. in Turbulence XII, Proc. 12th EUROMECH Eur. Turb. Conf., Marburg, 78 (Springer, New York 2009)
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John F. Gibson and Predrag Cvitanović
Geometry of turbulence in wall-bounded shear flows: a stroll through 61,506 dimensions
recommended
pdf Predrag Cvitanović and John F. Gibson
Geometry of turbulence in wall-bounded shear flows: Periodic orbits
Phys. Scr. T142, 014007 (2010)
seminar 3 streaming videos of Newton Inst presentations

Planes and pipes: technical papers

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Ashley P. Willis, Kimberly Y. Short and Predrag Cvitanović
Symmetry reduction in high dimensions, illustrated in a turbulent pipe
Phys. Rev. E 93, 022204 (2016) [ arXiv:1203.3701 ]

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Ashley P. Willis, Predrag Cvitanović and Marc Avila
Revealing the state space of turbulent pipe flow by symmetry reduction
J. Fluid Mech. 721, 514-540 (2013) [ arXiv:1203.3701 ]

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John F. Gibson, Jonathan Halcrow and Predrag Cvitanović
Visualizing the geometry of state space in plane Couette flow
J. Fluid Mech. 611, 107 (2008) [ arXiv:0705.3957 ]

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iPaper
John F. Gibson, Jonathan Halcrow,and Predrag Cvitanović
Equilibrium and traveling-wave solutions of plane Couette flow
J. Fluid Mech. 638, 243 (2009) [ arXiv:0808.3375 ]

iPaper Jonathan Halcrow, John F. Gibson, Predrag Cvitanović and Divakar Viswanath
Heteroclinic connections in plane Couette flow
J. Fluid Mech. 621, 365 (2009) [ arXiv:0808.1865 ]

iPaper Divakar Viswanath and Predrag Cvitanović
Stable manifolds and the transition to turbulence in pipe flow
J. Fluid Mech. 627, 215 (2009) [ arXiv:0801.1918 ]

State space geometry of Kuramoto-Sivashinsky flow

Explorations of weak turbulence described in terms of spatiotemporally recurrent patterns.

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Predrag Cvitanović, Ruslan L. Davidchack and Evangelos Siminos
On state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain
SIAM J. Appl. Dyn. Syst. 9, 1 (2010) [ arXiv:0709.2944 ]
pdf Yueheng Lan and Predrag Cvitanović
Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics
Phys. Rev. E 78, 026208 (2004) [ arXiv:0804.2474 ]
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Predrag Cvitanović, Freddy Christiansen and Vahtang Putkaradze
Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns
Nonlinearity 10, 50 (1997) [ chao-dyn/9606016 , NSF critique ]
star seminar Predrag Cvitanović and Y. Lan
Turbulence and what to do about it
(Bristol, Gottingen 2004 - PDF overheads)
star seminar Predrag Cvitanović
Spatiotemporal chaos in terms of unstable recurrent patterns
(overheads + streaming video (!), seminar abstract)
link Related links: Vachtang Putkaradze PhD thesis
The initial attempt: Vachtang's term paper toFix
Why ``Hopf's last hope'' in the title?


Symmetries of dynamical systems

How to quotient a symmetry of an equvariant dynamical system, rewrite the dynamics in the reduced, invariant coordinates.

This was meant to be a brief explanatory section in the ChaosBook.org chapter on trace formulas for systems with a continuous symmetry. Instead, I have gone the way of Marsdenites and am writing one paper after the other, each one looking very much like the preceeding one to a vulgar eye. Hopefully this all will eventually get digested into a single chapter of ChaosBook.org, and be done with.

pdf N. Burak Budanur and Predrag Cvitanović
Unstable manifolds of relative periodic orbits in the symmetry-reduced state space of the Kuramoto-Sivashinsky system
J. Stat. Phys. , (2016) [ arXiv:1509.08133 | ReadCube | DOI ]
pdf N. Burak Budanur, Predrag Cvitanović, Ruslan L. Davidchack and Evangelos Siminos
Reduction of the SO(2) symmetry for spatially extended dynamical systems
[ arXiv:1405.1096 ]
pdf Predrag Cvitanović, Daniel Borrero-Echeverry, Keith Carroll, Bryce Robbins and Evangelos Siminos
Cartography of high-dimensional flows: A visual guide to sections and slices
Chaos 22, 047506 (2012) [ arXiv:1209.4915 ]
Seminar Predrag Cvitanović
Got symmetry? here is how you slice it
Classics Illustrated version of the above paper.
pdf Stefan Froehlich and Predrag Cvitanović
Reduction of continuous symmetries of chaotic flows by the method of slices
Comm. Nonlinear Sci. and Numer. Simul. 17, 2074–2084 (2012) [doi:10.1016/j.cnsns.2011.07.007 , arXiv:1101.3037 ]
pdf Predrag Cvitanović, Ashley P. Willis and Marc Avila
Revealing the geometry of turbulent pipe flow attractor by symmetry reduction
in Jianxiang Wang, ed., Proceed. ICTAM 2012 Intern. Congr. Theor. and Appl. Mech. (2012) [ the long paper is here ]
pdf Evangelos Siminos and Predrag Cvitanović
Continuous symmetry reduction and return maps for high-dimensional flows
Physica D 240, 187-198 (2011) [ arXiv:1006.2362 ]
pdf Predrag Cvitanović
Relativity for cyclists
ChaosBook.org
A (hopefully) pedagogical overview of the symmetry reduction methods.
Seminar Predrag Cvitanović
Continuous symmetry reduction for high-dimensional flows
Attempt to motivate the need for symmetry reduction, and the available methods in a few slides.
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Predrag Cvitanović
Continuous symmetry reduced trace formulas
(in preparation, July 2006)
Why is this paper not published yet? I would like at least one person out there in the universe to understand it before submitting it. Seems to be a high treshold.
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Predrag Cvitanović and Bruno Eckhardt
Symmetry decomposition of chaotic dynamics
Nonlinearity 6, 277 (1993) [ chao-dyn/9303016 ]
in part superceeded by ChaosBook.org: World in a mirror

Modulated amplitude waves

Getting hang of spatiotemporal dynamics in nearly integrable regimes, as a warmup to turbulent dynamics...

pdf Mason A. Porter and Predrag Cvitanović
A perturbative analysis of Modulated Amplitude Waves in Bose-Einstein Condensates
CHAOS 14, 739 (2004) [ nlin.CD/0308024 ]

pdf Mason A. Porter and Predrag Cvitanović
Modulated Amplitude Waves in Bose-Einstein Condensates
Phys. Rev. E 69, 047201 (2004) [ nlin.CD/0307032 ]

pdf Yueheng Lan, Nicola Garnier and Predrag Cvitanović
Modulated solutions of the complex Ginzburg-Landau equation
Physica D 188 193, (2004) [ nlin.PS/0208001 ]

Noise is your friend

The noise that physical systems are affected by limits the resolution that can be attained in partitioning their state space. We determine the `finest attainable' partition and replace the Fokker-Planck evolution is by a finite matrix.

pdf Jeffrey M. Heninger, Domenico Lippolis and Predrag Cvitanović
Perturbation theory for the Fokker-Planck operator in chaos
[ arXiv:1507.00462 ]
pdf Jeffrey M. Heninger, Domenico Lippolis and Predrag Cvitanović
Neighborhoods of periodic orbits and the stationary distribution of a stochastic chaotic systems
Phys. Rev. E. 92 062922, (2015) [ arXiv:1507.00462 ]
pdf Predrag Cvitanović and Domenico Lippolis
Knowing when to stop: How noise frees us from determinism
in M. Robnik and V.G. Romanovski, eds., Let's Face Chaos through Nonlinear Dynamics, pp. 82--126 (Am. Inst. of Phys., Melville, New York, 2012) [ arXiv:1206.5506 ]
Seminar Predrag Cvitanović
Physicist's life is intractable
Intractability workshop: "Counting, Inference, and Optimization on Graphs",
2 nov 2011 (talk aimed at computer scientists)
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video of the intractable lecture (pretty clear on the interplay of noise and determinism - recommended)
pdf Domenico Lippolis and Predrag Cvitanović
How well can one resolve the state space of a chaotic flow?
Phys. Rev. Lett. 104, 014101 (2010) [ arXiv:0902.4269 ]
Seminar Predrag Cvitanović and Domenico Lippolis
How well can one resolve the state space of a chaotic flow?
SIAM Snowbird Dynamical Systems 2011 talk.

A triptych of technical papers whose goal is to develop improved methods of computing higher order corrections to nontrivial saddles of path integrals:

pdf Predrag Cvitanović, Carl P. Dettmann, Ronnie Mainieri and Gábor Vattay
Trace formulas for stochastic evolution operators: Weak noise perturbation theory
J. Stat. Phys. 93, 981 (1998) [ chao-dyn/9807034 ]

pdf Predrag Cvitanović, Carl P. Dettmann, Ronnie Mainieri and Gábor Vattay
Trace formulas for stochastic evolution operators: Smooth conjugation method
Nonlinearity 12, 939 (1999) [ ps.gz published version , ps.gz , chao-dyn/9811003 ]

pdf Predrag Cvitanović, Carl P. Dettmann, G. Palla, Niels Søndergaard and Gábor Vattay
Spectrum of stochastic evolution operators: Local matrix representation approach
Phys. Rev. E 60, 3936 (1999) [ ps.gz , chao-dyn/9904027 ]

Seminar Predrag Cvitanović
Trace formulas for stochastic evolution operators toFix
(seminar abstract, 1999).
Seminar Predrag Cvitanović
Noisy Chaos
a talk at Hans C. Fogedby 60 symposium.

Wave chaos in elastodynamics

A step toward generalizing Gutzwiller semiclassical theory to wave chaos in elastodynamical systems (professionals do not allow us to call this "acoustics")

pdf Predrag Cvitanović, Niels Søndergaard and Andreas Wirzba
Wave Chaos in Elastodynamic Cavity Scattering
Europhysics Letters 72, 534 (2005)
Brief history: submitted to Phys Rev Letters Aug 28 2001; revised version submitted May 18 2004; referee offended by the "In elastodynamics, period two implies chaos" title - rejected; submitted to Europhysics Letters, May 2005, revised version with more resonances included Sep 23 2005, accepted Sep 26 2005.
[ nlin/0108053 ]
Related links:
link Niels Søndergaard, Predrag Cvitanović, and Andreas Wirzba,
Closed complex rays in scattering from elastic voids
in B. Nilsson, ed., Mathematical Modelling of Wave Phenomena 2005, AIP Conference Proceedings (2006)
Niels Søndergaard, PhD thesis (Dec 2000)
seminar Andreas Wirzba, Georgia Tech seminar (Aug 2001)

Periodic orbit extraction

How to compute Floquet exponents that differen by 1000's of orders of magnitude (a step toward determining physical dimension of inertial manifolds):

pdf Xiong Ding and Predrag Cvitanović
Periodic eigendecomposition and its application in Kuramoto-Sivashinsky system
[ arXiv.org:1406.4885 ]

A variational principle for robust periodic orbit and invariant tori searches:

pdf Yueheng Lan, Cristel Chandre, and Predrag Cvitanović
Variational method for locating invariant tori
Phys. Rev. E 74, 046206 (2006) [ arXiv.org:nlin.CD/0508026 ]
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Predrag Cvitanović and Yueheng Lan
Turbulent fields and their recurrences
in N. Antoniou, ed., Proceed. of 10. Intern. Workshop on Multiparticle Production: Correlations and Fluctuations in QCD (World Scientific, Singapore 2003); [ nlin.CD/0308006 ]
pdf Yueheng Lan and Predrag Cvitanović
Variational method for finding periodic orbits in a general flow
Phys. Rev. E 69, 016217 (2004) [ nlin.CD/0308008 , ps.gz ]


Periodic orbit extraction from data

An early proposal on how to fish for periodic orbits by looking for near recurrences:

pdf D. Auerbach, Predrag Cvitanović, Jean-Pierre Eckmann, Gemunu Gunaratne and Itamar Procaccia
Exploring chaotic motion through periodic orbits
Phys. Rev. Lett. 58, 2387-2389 (1987)

An attempt to demonstrate existence of unstable periodic orbits and chaos in a slices of rat brains, very noisy neurophysiology experimental data

pdf Marc W. Slutzky, Predrag Cvitanović and David J. Mogul
Deterministic chaos and noise in three in vitro hippocampal models of epilepsy
Annals of Biomedical Engineering 29, 607 (2001).
pdf Marc W. Slutzky, Predrag Cvitanović and David J. Mogul
Manipulating epileptiform bursting in the rat hippocampus using chaos control and adaptive techniques
IEEE Transactions on Biomedical Engineering 50, 559 (2001).
pdf Marc W. Slutzky, Predrag Cvitanović and David J. Mogul
Identification of determinism in noisy neuronal systems
J. Neuroscience Methods 118, 153 (2002)
iPaper Marc W. Slutzky, David J. Mogul and Predrag Cvitanović
Chaos control of epileptiform bursting in the brain
in Control of chaos in nonlinear circuits and systems, by B. W.-K. Ling, H. H.-C. Iu, and H.-K. Lam, eds., (World Scientific, Singapore 2009)

Kill periodic orbit theory:

Two papers demonstrating that periodic orbits must satisfy infinitely many sum rules

pdf Predrag Cvitanović, Kim Hansen, Juri Rolf and Gabor Vattay
Beyond periodic orbit theory
Nonlinearity 11, 1209 (1998) [ ps.gz ]
pdf Sune F. Nielsen, Per Dahlqvist and Predrag Cvitanović
Periodic orbit sum rules for billiards: Accelerating cycle expansions
J. Phys. A 32, 6757 (1999) [ ps.gz , chao-dyn/9901001 , working notes ]

Nonhyperbolic dynamics

Non-hyperbolicity, intermittency, power-law correlations: convergence of cycle expansions, analyticity of dynamical zeta functions, approach to the border of order by renormalization methods.

pdf Roberto Artuso, Predrag Cvitanović and Gregor Tanner
Cycle expansions for intermittent maps
Proc. Theo. Phys. Supp. 150, 1 (2003) [ nlin.CD/0305008 ]
[most of this paper is incorporated in ChaosBook.org]
pdf Carl P. Dettmann and Predrag Cvitanović
Cycle expansions for intermittent diffusion
Phys. Rev. E 56, 6687 (1997)
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Roberto Artuso, Erik Aurell and Predrag Cvitanović
Recycling of strange sets: II. applications
Nonlinearity 3, 361 (1990)

Deterministic diffusion

Periodic orbit theory of deterministic diffusion

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Predrag Cvitanović, Jean-Pierre Eckmann and Pierre Gaspard
Transport properties of the Lorentz gas in terms of periodic orbits
Chaos, Solitons and Fractals 6, 113 (1995) - (61 kB) [ ps.gz ]
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Predrag Cvitanović, Pierre Gaspard and Thomas Schreiber
Investigation of the Lorentz Gas in terms of periodic orbits
CHAOS 2, 85 (1992)


Periodic orbit theory of diffusion extended to power spectra, with Pikovsky and Feigenbaum. Both Mitchell's draft and Arkady's draft have interesting material not in the published, abreviated version:

pdf Predrag Cvitanović and Arkady S. Pikovsky
Cycle expansion for power spectrum
Proc. SPIE - Int. Soc. Opt. Eng. (USA) 2038, 290 (1997)

Cycle expansions

How to implement the periodic orbit theory as a computational method

ps Predrag Cvitanović
Trace formulas in classical dynamical systems
in I.V. Lerner, J.P. Keating, D.E. Khmelnitskii, eds., Supersymmetry and Trace Formulae: Chaos and Disorder, (Plenum, New York 1998)
pdf Gábor Simon, Predrag Cvitanović, Mogens T. Levinsen, I. Csabai and Á. Horváth
Periodic orbit theory applied to a chaotically oscillating gas bubble in water
Nonlinearity 15, 25 (2002)
Predrag Cvitanović, Gábor Vattay and Andreas Wirzba
Quantum fluids and classical determinants
in H. Friedrich and B. Gerhardt., eds., Classical, Semiclassical and Quantum Dynamics in Atoms - in Memory of Dieter Wintgen, Lecture Notes in Physics 485 (Springer, New York 1997) [ ps.gz , chao-dyn/9608012 ]
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Predrag Cvitanović
Dynamical averaging in terms of periodic orbits
Physica D 83, 109 (1995)
[most of this paper is incorporated in ChaosBook.org]
Neal J. Balmforth, Predrag Cvitanović, Glenn R. Ierley, Edward A. Spiegel and Gabor Vattay
Advection of vector fields by chaotic flows
in Stochastic Processes in Astrophysics, Annals of New York Academy of Sciences 706, 148 (1993) [ ps.gz , chao-dyn/9307011 - sorry, no figures ]
pdf Freddy Christiansen and Predrag Cvitanović
Periodic orbit quantization of the anisotropic Kepler problem
CHAOS 2, 61 (1992)
pdf Periodic orbit theory in classical and quantum mechanics, CHAOS 2, 1 (1992)
pdf Kvantekaos, KVANT 5, 1 (1994) [e-print not available]
pdf Kvantes Lykkelige Dag (with Kenneth Krabat), Naturligvis 20 (1991) [e-print not available]
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Predrag Cvitanović and Bruno Eckhardt
Periodic orbit expansions for classical smooth flows
J. Phys A 24, L237 (1991) [ preprint ]
pdf Freddy Christiansen, Predrag Cvitanović and Hans Henrik Rugh
The spectrum of the period-doubling operator in terms of cycles
J. Phys A 23, L713 (1990)
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Predrag Cvitanović and Bruno Eckhardt
Periodic orbit quantization of chaotic systems
Phys. Rev. Lett. 63, 823 (1989)

The two in-depth papers on cycle expansions combine Artuso and Aurell PhD theses with several years of my own work - mostly incorporated into ChaosBook.org since. Nobody reads the second paper, which is a pity - there is some good stuff there.

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Roberto Artuso, Erik Aurell and Predrag Cvitanović
Recycling of strange sets: I. cycle expansions
Nonlinearity 3, 325 (1990)

The first paper on cycle expansions:

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Predrag Cvitanović
Invariant measurement of strange sets in terms of cycles
Phys. Rev. Lett. 61, 2729 (1988)

Quantum determinants

For nice hyperbolic systems Fredhollm determinats are entire, but the Gutzwiller-Voros zeta functions have poles. In 1992 we conjectured a "quantum Fredholm determinant" and showed that it has a larger radius of analiticity than the Gutzwiller-Voros zeta function. Extension of the evolution from phase space to phase space together with the tangent space enables us to construct a multiplicative "quasiclassical evolution operator" and the associated (entire) "quasiclassical zeta function". Unfortunatelly this zeta function has extraneous "classical" eigenvalues, and is not useful in practice. Restriciting its function space to purely quantum spectrum remains an open problem.

Predrag Cvitanović, Gábor Vattay and Andreas Wirzba
Quantum fluids and classical determinants
in H. Friedrich and B. Gerhardt., eds., Classical, Semiclassical and Quantum Dynamics in Atoms - in Memory of Dieter Wintgen, Lecture Notes in Physics 485 (Springer, New York 1997) [ ps.gz , chao-dyn/9608012 ]
Predrag Cvitanović, Bruno Eckhardt, Per E. Rosenqvist, Gunnar Russberg and P. Scherer
Pinball scattering
in G. Casati and B. Chirikov, eds., Quantum Chaos, (Cambridge University Press, Cambridge 1994) [ ps.gz - sorry, no figures ]
pdf Predrag Cvitanović and Gábor Vattay
Entire Fredholm determinants for evaluation of semi-classical and thermodynamical spectra
Phys. Rev. Lett. 71, 4138 (1993) [ chao-dyn/9307012 ]
pdf Predrag Cvitanović, Per E. Rosenqvist, Gábor Vattay, and Hans H. Rugh
A Fredholm determinant for semi-classical quantization
CHAOS 3, 619 (1993) [ ps , chao-dyn/9307014 ]
pdf Predrag Cvitanović and Per E. Rosenqvist
A new determinant for quantum chaos
in G.F. Dell'Antonio, S. Fantoni and V.R. Manfredi, eds., From Classical to Quantum Chaos, Soc. Italiana di Fisica Conf. Proceed. 41, pp. 57-64 (Ed. Compositori, Bologna 1993)

Geometry of chaos

How to partition the phase space of a chaotic dynamical system

pdf Mason A. Porter and Predrag Cvitanović
Ground Control to Niels Bohr: Exploring Outer Space with Atomic Physics
Notices Am. Math. Soc. 52, 1020 (2005) [ physics/0505085 , pdf ]
Featured in: Science News 168 MSNotices200509.html (Sep 10 2005); American Mathematical Society Notices 52 (Oct 2005)

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Predrag Cvitanović
Periodic orbits as the skeleton of classical and quantum chaos
Physica D 51 138 (1991)
[most of this paper is incorporated in ChaosBook.org]

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Predrag Cvitanović, Gemunu H. Gunaratne and Itamar Procaccia
Topological and metric properties of Hénon-type attractors
Phys. Rev. A 38, 1503 (1988)
[the non-Procaccian, non-gibberish part of this paper is incorporated in ChaosBook.org]

pdf Predrag Cvitanović and Kai T. Hansen
Bifurcation structures in maps of Hénon type
Nonlinearity 11, 1233 (1998)
[the best exposition of physicist's pruning front theory is possibly still Kai T. Hansen 1993 Ph.D. thesis, Symbolic dynamics in chaotic systems]

pdf Kai T. Hansen and Predrag Cvitanović
Symbolic Dynamics and Markov Partitions for the Stadium Billiard
J. Stat. Phys. ? (20??) [ chao-dyn/9502005 ]

The archived version was accepted for publication by J. Stat. Phys. in 1996, but then I had a brilliant idea how to make it better, and a revised version is still waiting to be resubmitted. If you can bring it back to a publishable state - current version is Notes for Kai (sept 95) - please do it, and join us as a co-author. The paper is as good as most stuff that gets published, but neither of us has the time to finish it.



Predrag Cvitanović: transitions to chaos publications

[ period doubling theory | renormalization the complex plane | circle map renormalization | phase transitions ]

starstar Renormalization in chaos research overview

Renormalizaton theory of transitions to chaos

A very brief history of universality in period doubling

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Predrag Cvitanović
Universality in chaos (or, Feigenbaum for cyclists)
lectures given at 1982 Zakopane School of Theoretical Physics,
Acta Phys. Polonica A65, 203 (1984) [ scan by Chi-Keung Wong ]
pdf Predrag Cvitanović and Mogens H. Jensen
Universality in transitions to chaos
in Chaos and universality (Nordita reprint selection, November 1981)
pdf Predrag Cvitanović and Mogens H. Jensen
Universalitet i overgang til kaos
Fysisk Tidsskrift 80, 82 (1982)


Circle map renormalization

ps Predrag Cvitanović
Circle maps: irrationally winding,
in C. Itzykson, P. Moussa and M. Waldschmidt, eds., Number Theory and Physics, Les Houches 1989 Spring School, (Springer, New York 1992)
- sorry, no figures
[most of this paper is incorporated in ChaosBook.org]
pdf Predrag Cvitanović, Gemunu H. Gunaratne and M.J. Vinson
On the mode-locking universality for critical circle maps
Nonlinearity 3, 873 (1990)
pdf Predrag Cvitanović, Mogens H. Jensen, Leo P. Kadanoff and Itamar Procaccia
Renormalization, unstable manifolds and the fractal structure of mode locking
Phys. Rev. Lett. 55, 343 (1985)
pdf Predrag Cvitanović
Farey organization of the fractional Hall effect
Phys. Scr. T9, 202 (1984)
pdf Predrag Cvitanović
Universal scaling laws for maps on the interval and circle maps
in R.W. Boyd, L.M. Narducci and M.G. Raymer, eds., Instabilities and Dynamics of Lasers and Nonlinear Optical Systems, (U. of Cambridge Press, Cambridge, 1985)
pdf Predrag Cvitanović, B. Shraiman and Bo Söderberg
Scaling laws for mode lockings in circle maps
Phys. Scripta 32, 263 (1985)
pdf Predrag Cvitanović, Mogens H. Jensen, L.P. Kadanoff and Itamar Procaccia
Circle maps in the complex plane
in L. Pietronero and E. Tosatti, eds., Fractals in Physics, Trieste, July 1985 (North Holland, New York, 1985)
pdf Predrag Cvitanović and Tomas Bohr
Chaos is good news for physics
Nature 329, 391-392 (1987)
pdf Predrag Cvitanović
Chaos for cyclists
in E. Moss, ed., Noise and Chaos in Nonlinear Dynamical Systems, (Cambridge Univ. Press, Cambridge 1989)
ps Predrag Cvitanović
Recycling chaos
in A. Ferraz, F. Oliveira and R. Osorio, eds., Nonlinear Physical Phenomena, Brasilia 1989 Winter School, (World Scientific, Singapore 1990) - sorry, no figures
ps Predrag Cvitanović
The power of chaos
in J.H. Kim and J. Stringer, eds., Applied Chaos, (John Wiley & Sons, New York 1992) - sorry, no figures


Renormalization theory in the complex plane

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Predrag Cvitanović and Jan Myrheim
Complex universality
Comm. Math. Phys. 121, 225 (1989)

pdf Predrag Cvitanović and Jan Myrheim
Universality for period n-tuplings in complex mappings
Phys. Lett. 94A, 329 (1983)

pdf Predrag Cvitanović
Renormalization description of transitions to chaos
in S. Lundquist, N.H. March and E. Tosatti, eds., Order and Chaos in Non-linear Physical Systems, pp. 73-97 (Plenum, New York 1988) - a subset of the "Complex Universality" paper

pdf Predrag Cvitanović, Tomas Bohr and Mogens H. Jensen
Fractal aggregates in the complex plane
Europhys. Lett. 6, 445 (1988)


Phase transitions on fractal sets

The discovery of phase transitions on "strange sets" was followed up by many other authors; such transitions were subsequently found in a variety of dynamical systems.

pdf Predrag Cvitanović, Roberto Artuso and Brian Kenny
Phase transitions on strange irrational sets
Phys. Rev. A 39, 268 (1989)

pdf Predrag Cvitanović
Hausdorff dimension of irrational windings
in R. Gilmore, ed., Proceedings of the XV International Colloquium on Group Theoretical Methods in Physics, pp. 184-198 (World Scientific, Singapore, 1987)

pdf Predrag Cvitanović
Phase transitions on strange sets,
in P. Zweifel, G. Gallavotti and M. Anile, eds., Non-linear Evolution and Chaotic Phenomena, pp. 349-361 (Plenum, New York 1988) - sorry, not scanned yet



Predrag Cvitanović: group theory publications

www overview
for my group theory publications click here
Group theory webbook

pdf Predrag Cvitanovic´
Negative dimensions and E7 symmetry
Nucl. Phys. B188, 373--396 (1981) [ SPIRES citations ]
please click here for the background story

pdf Predrag Cvitanovic´
Group theory for Feynman diagrams in non-Abelian gauge theories
Phys. Rev. D 14, 1536 (1976) [ INSPIRE, Google Scholar ]



Predrag Cvitanović: quantum field theory publications

[ turbulent field theory | perturbative QED | finiteness conjecture | planar field theory | perturbative QCD | phenomenology ]

INSPIRE citation search

Turbulent field theory

Program whose goal is a non-perturbative theory of turbulent dynamics of classical, stochastic and quantum fields. Turbulent field theory is developed in two directions:
1) explorations of the feasibility of describing weak turbulence in terms of spatiotemporally recurrent patterns, and
2) new perturbation theory methods for computing corrections about nontrivial saddles of path integrals.

Read the sketch paper first, click through the trace formulas papers next.


Perturbative QED

One big calculation, the answer

\begin{displaymath}
{1 \over 2} (g-2) = {1 \over 2} {\alpha \over \pi}
- 0.3284...
...ght)^2
+ (1.183 \pm 0.011) \left({\alpha \over \pi}\right)^3.
\end{displaymath}

and why did I do this? The electron magnetic moment is the most precise prediction of quantum field theory, and its most precise experimental test. It is also the simplest physical quantity on which to test ideas about the convergence of QED perturbation theory.

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Predrag Cvitanovic´ and Toichiro Kinoshita
Feynman-Dyson rules in parametric space
Phys. Rev. D10, 3478 (1974) [ INSPIRE citations ]

A (hopefully) pedagogical overview of the Schwinger and Feynman parametric representation of Feynman integrals, should be useful for any QFT perturbative calculation. Some new results, for example the theorem derived in the appendix.

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Predrag Cvitanovic´ and Toichiro Kinoshita
New approach to the separation of ultraviolet and infrared divergences of Feynman-parametric integrals
Phys. Rev. D10, 3991 (1974) [ INSPIRE citations ]

A new method for dealing with Feynman diagram infrared divergences is introduced. The main result are the very ellegant and compact formulas (3.40) and (5.14) which extract the finite part from any general mass-shell Feynman diagram, removing both ultraviolet and infrared parts of the diagram and all of its counterterms. What remains after the projection is a pointwise-convergent integrand, well suited to numerical integrations.

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Predrag Cvitanovic´ and Toichiro Kinoshita
Sixth-order radiative corrections to the electron magnetic moment
Phys. Rev. Lett. 29, 1534 (1972)

At the time perhaps the most demanding numerical computation in theoretical physics, it remained QED's most precise prediction for a number of years. A step in T. Kinoshita's heroic undertaking, but nothing you would want to read today.

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Predrag Cvitanovic´ and Toichiro Kinoshita
Sixth order magnetic moment of the electron
Phys. Rev. D10, 4007 (1974) [ INSPIRE citations ]

Most of this you can safely skip, unless you happen to be evaluating (g-2) to 3-loop level.

However, the new formula (6.22) for the electron magnetic moment, Sect. VI, might be of interest: (g-2) is evaluated from a derivative of the 2-point electron self-energy, rather than a 3-point electron-photon vertex, with fewer Feynman graphs:
(1) it enabled us to calculate the electron magnetic moment by two wholy independent methods.

no file Predrag Cvitanovic´
Computer generation of integrands for Feynman parametric integrals
Cornell preprint CLNS-234 (June, 1973) and Proc. 3rd Coll. on Advanced Comp. Meth. in Theoretical Physics (Marseille, 1973)

One of the ur-algebraic symbol manipulation programs



Finiteness of gauge field theories

For me the conceptually most striking lesson of these long QED calculations were the amazing cancellations induced by gauge invariance. The desire to understand and exploit gauge invariance more effectively has motivated much of my subsequent research. The most interesting results of this effort were the mass-shell QCD Ward identities and the construction of the QCD gauge sets. This work also motivated the formulation of planar field theory.

Other papers in this series are those on the QCD mass-shell infrared singularities and the diagram counting, both attempts to formulate gauge-invariant models computable to high orders, in order to investigate the nature of gauge-invariance induced cancellations.

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Predrag Cvitanovic´
Asymptotic estimates and gauge invariance
Nucl. Phys. B127, 176 (1977) [ INSPIRE citations ]

On basis of very skimpy numerical evidence, I conjecture that the gauge invariance induced cancellations are so dramatic that the growth rate of high order perturbation theory corrections to mass-shell gauge-invariant quantities is slower than Dyson's asymptotic series n! estimate. In the case of QED vertex corrections, the smallest gauge invariant set contributing to (m+m'+k)th order consists of m photon "strands" attached to the incoming electron, m' photon "strands" attached to the outgoing electron, and k photon "strands" crossing the external photon vertex. Ignoring sets with electron loops and assuming that each gauge set gives a finite contribution leads to a guess that perturbation series for the electron magnetic moment sums up to approximately

\begin{displaymath}
{1 \over 2} (g-2) = {1 \over 2} {\alpha \over \pi}
{ 1 \ov...
...ha \over \pi}\right)^2
\right)^2
} + \mbox{\lq\lq corrections''}.
\end{displaymath}
The story behind the conjecture.



Planar field theory

The method that I have used to develop the planar field theory is somewhat different from what is in most field theory textbooks; consulting my Field Theory webbook might make this derivation more accessible.

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Predrag Cvitanovic´
Planar perturbation expansion
Phys. Lett. B99, 49 (1981) [ INSPIRE citations ]
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Predrag Cvitanovic´
The planar sector of field theories (with P.G. Lauwers and P.N. Scharbach),
Nucl. Phys. B203, 385 (1982) [ INSPIRE citations ]

Though the formalism is rather different, essentially the same theory was rederived in 1994 by M.A. Douglas, R. Gopakumar and David J. Gross, D.V. Voiculescu, in 1998 by 't Hooft, and many others. R. Speicher (13 Apr 2014): "In a sense some aspects of this theory of freeness were anticipated (but mostly neglected) in the physics community in [this] paper"


Perturbative QCD


pdf Predrag Cvitanovic´
Yang-Mills theory of the mass-shell
Phys. Rev. Lett. 37, 1528 (1976) [ INSPIRE citations ]

Mass-shell amplitudes for both QED and QCD are defined via dimensional regularization, and shown to to be gauge invariant trough a cancellation between UL and IR singularities. Prior to this article, IR and UR were regularized by different methods which, when applied to QCD, violated gauge invariance.

pdf Predrag Cvitanovic´
Infra-red structure of Yang-Mills theories
Phys. Lett. 65B, 272 (1976) [ INSPIRE citations ]

pdf Predrag Cvitanovic´
Quantum Chromodynamics on the mass-shell
Nucl. Phys. B130, 114 (1977) [ INSPIRE citations ]

pdf Predrag Cvitanovic´, Benny Lautrup and R.B. Pearson
The number and weights of Feynman diagrams
Phys. Rev. D18, 1939 (1978) [ INSPIRE citations ]

no file Predrag Cvitanovic´, Jeff Greensite and Benny Lautrup
The cross-over points in lattice gauge theories with continuous gauge groups
Phys. Lett. 105B, 201 (1981) [ INSPIRE citations ]

pdf Predrag Cvitanovic´, P.G. Lauwers and P.N. Scharbach
Gauge invariance structure of Quantum Chromodynamics
Nucl. Phys. B186, 165 (1981) [ INSPIRE citations ]


Phenomenology etc.

pdf Predrag Cvitanovic´
Spin and parity from crossections and angular distributions,
in J. Bjorken et al., Notes from the SLAC Theory Workshop on the Psi, SLAC-PUB-1515 , (Dec. 7, 1974)
no file Predrag Cvitanovic´
Wide-angle behavior of a double-scattering diagram
Phys. Rev. D10, 338 (1974)
no file Predrag Cvitanovic´, R.J. Gonsales and D.E. Neville
Color charge algebras in Adler's Chromodynamics
Phys. Rev. D18, 3881 (1978)
no file Predrag Cvitanovic´, P. Hoyer and K. Konishi
Partons and branching
Phys. Lett. 85B 413 (1979)
no file Predrag Cvitanovic´ and R. Horsley
Exact solutions of the Altarelli-Parisi equations
Nucl. Phys. B173, 229 (1980)
no file Predrag Cvitanovic´, Poul Hoyer and K. Zalewski
Parton evolution as a branching process
Nucl. Phys. B176, 429 (1980) [ INSPIRE citations ]

Miscelaneous

no file Predrag Cvitanovic´ et al
drafts in progress (of interest only to frustrated collaborators)

pdf Predrag Cvitanović
Midnight rider
Bike World (August 1974)

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Predrag Cvitanović and Mitchell J. Feigenbaum, for David Bensimon, Thomas C. Halsey, Mogens H. Jensen, Leo P. Kadanoff, Albert Libchaber, Itamar Procaccia, Boris I. Shraiman and Joel Stavans
More on microcanonical paradigm
(Göteborg, 3 a.m. of 17 Nov. 1985), rejected from every proceedings submitted to.