Predrag Apr 4 2004 Thesis goals: weakly turbulent Kuramoto-Sivashinsky * KS covering symbolic dynamics, * good numerical estimates of mean wavelength (in x direction), * mean time between dislocations (in t direction), * clear discussion of symmetry reduced symbolic dynamics, * 10-100 cycles on each fixed wavelength reppeling pruned horseshoe, * a clear cycle expansion definition of * the mean wavelength (in x direction), * mean time between dislocations (in t direction), * 2-20 cycles that connect the two sets * an estimate of the mean time between dislocations