|Week 7 overview|
- 13. The spatial ordering of trajectories from the time ordered itineraries
- 14. Qualitative dynamics, for cyclists
- Homework 7
Qualitative dynamics: (i) temporal ordering, or itinerary with which a trajectory visits state space regions and (ii) the spatial ordering between trajectory points, the key to determining the admissibility of an orbit with a prescribed itinerary. Kneading theory.
Dynamical partitioning of a plane. Stable/unstable invariant manifolds, and how they partition the state space in intrinsic, topologically invariant manner. Henon map is the simplest example.
|Charting the state space|
|Discussion forum for week 7|
Chapter Charting the state space
Study sect. 14.6 Symbolic dynamics, basic notions.
Eye candy: Chaos in Heavens
(and a lesson: you will never understand anything by staring at projections of chaotic trajectories onto configuration coordinates - you need to take care of symmetries, look for equilibria, construct Poincare sections, ...)
Chaos VI - Smale in Copacabana
CHAOS, a math movie with nine 13-minute chapters