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Introduction to
Nonlinear Dynamics and Chaos
svn: $Author: predrag $  $Date: 20070611 09:54:53 0400 (Mon, 11 Jun 2007) $
Course Schedule
Part I: Complex motion, unusual geometry
 January 9
1. A brief history of motion in time

The introductory lecture (as well as many to follow) will complement the
material covered in the textbook.
Reading: Chapter 1
Optional reading:
overheads (first lecture pictures)
ChaosBook.org Brief history
of chaos
might amuse you.
 January 11
2.
Fractal objects

Lecture will complement the material covered in the textbook.
Reading: all of Chapter 2 except sections 2.2.2, 2.2.3
Problem set 1:
2.1, 2.8, 2.15,
2.16
(solutions)
 January 15
Institute holiday  MLK Day
Part II: Introductory concepts
 January 16
3. Regular motion
 Reading: Chapter 3,
sections
3.1, 3.2
 January 18
4. Regular motion
 Reading: Chapter 3,
sections
3.3, 3.4, 3.5
Problem set 2:
3.1, 3.2,
3.7,
3.15,
3.22,
3.4,
3.8
(solutions)
 January 23
5. Regular motion
 Reading:
Chapter 3, section 3.5.2
 January 25
6. Driven motion
 Reading:
Chapter 4, sections 4.1, 4.2;
Appendix A.1.1
Problem set 3:
3.24,
4.2,
4.3,
3.23
(solutions)
 January 30
7. Driven motion
 Reading:
Chapter 4, section 4.3;
Appendix A.1.2
 February 1
8. 2 and 3d flows and maps summarized
 Reading: Chapter 4, sections 4.4  4.8
Optional reading:
analytic example (not in the book)
Problem set 4:
4.5, 4.8, 4.9, 4.11,
4.7
(solutions)
Part III: Investigation of chaotic motion
 February 6
9. Chaos in dissipative systems
 Reading: Chapter 5, sections 5.1, 5.2
Optional reading:
Game of pinball (grateful for any suggestions
how to improve this, edits, ...)
 February 8
 guest lecture by
Rytis Paškauskas
10. Baker map
 Reading: Chapter 5, sections 5.35.2.2
Problem set 5

(solutions)
bonus problem 27.2

(solution)
 February 13
11. Homoclinic tangle
 Reading: any other book, for example Ott or
scholarpedia.org (if you find something good, let me know)
 February 15
12. Lozi map
 Reading: Chapter 5,
5.2.4  5.2.6 (skip section 5.2.3)
Problem set 6

(solutions, preliminary)
 February 20
13. Universality in chaos
 Reading: Chapter 5, section 5.3
 February 22
14. Midterm
exam

reading list
 problem 1
 problems 2,3 and solutions
No problem set this week.
 February 27
 NOTE: 9:15am undergrads meeting
15. Universality in chaos
 Reading: Chapter 5, section 5.3;
Universality in transitions to
chaos
[2p. per page version]
(grateful for any suggestions
how to improve this, edits, ...)
 March 1
16. From 3d flows
to 1d maps
 Reading:
Rossler system
Problem set 7: exercises
1, 2, 4,
3;
bonus points for all:
exercise 5. Compute stability eigenvalues of the two equilibria.
exercise 7. Intrinsically parametrized Rossler map (a good solution set
goes straight into ChaosBook.org)
Do not copy Rytis  do your own, it will be simpler.
 March 6
17. Return maps, period doubling
 March 8
18. Measures of chaos
 Reading: Section 5.4, skip 5.4.3, 5.4.6
Problem set 8,
exercise 26.1

(solutions)
 March 13
19. Natural measures
 Reading: Section 5.5
 March 15
20. Measures of chaos
 Reading: Chapter 5, p. 186, box 5.6; skip sections 5.6, 5.7
Reading:
Transporting densities, sections 9.1, 9.2, 9.3
Problem set 9:
5.35,
5.34;
bonuspoints problem for everybody:
exercise 9.5
(solutions ,
solution to 9.5)
 March 1923
Midterm recess
 March 27
21. Transient chaos
 Reading: Chapter 6, section 6.1, 6.2, 6.3; skip fractal dimensions
parts, as well as section 6.3.3
 March 29
22. Horseshoes
 Reading: Chapter 6, sections 6.4, 6.5
Problem set 10:
6.1, 6.2,
6.10
(solutions)
 April 3
23. Putting order into chaos
 Reading: Qualitative dynamics, for pedestrians,
sections 11.3, 11.4
Optional reading: How Dame Mary L. Cartwright discovered chaos in 1940's.
 April 5
24. Conservative chaos

Reading: Chapter 7, sections 7.1, 7.2
Problem set 11:
11.1, 11.6,
11.7;
bonuspoints problem for everybody:
12.1
(solutions,
solution to 11.7)
 April 10
25. Combinatorics, prime cycles

Reading: Chapter 7, section 7.3
 April 12
26. Standard map, diffusion, KAM

Reading: Chapter 7  read section 7.4, but skip the algebra;
sections 7.5, 7.6, 7.7
Problem set 12:
11.7 (well executed parts (b) and (f)
might earn bunch of bonus points
and your immortalization in ChaosBook.org);
7.2, 7.4,
7.8;
bonuspoints problem for everybody:
7.9
how to contribute figures to ChaosBook.org
(solutions)
 April 17
27. Chaotic scattering
 Reading: Chapter 8, sections 8.1, 8.2, skip the rest
Optional reading: high school geometry version
 April 19
28. Turbulence
 April 24
29. Nonlinear locomotion, nonlinear heart
 No reading: decerebrated frogs, giant squids and
dog hearts

takehome final exam
 Reading: Turbulence?
Demo of KuramotoSivashinsky simulations, by
Ruslan L. Davidchack
 April 26
30. Brain: do not leave home without it
 No reading, freebie lecture:
 "Decoding Neural Signals for the Control of Movement", by
Solla, Rebesco, Miller and Hatsopoulos
 Friday Apr 27
classes end

takehome final exam
due no later than
10:50am Thu, May 3
delivered either to Jonathan or Predrag, 5th floor Howey
(solution by Matt Marshall)
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grades deadline Mon, May 7
Predrag Cvitanović