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gtspring2009:schedule:sections_orbits [2009/04/10 08:10]
gibson
gtspring2009:schedule:sections_orbits [2010/02/02 07:55]
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-====== April 14 study group ====== 
  
-Some topics I would like to discuss. Feel free to add your own. 
- 
-===== Poincare sections and periodic orbits ===== 
- 
-Dustin and I have just begun producing Poincare sections of the unstable manifold ​ 
-around the Nagata upper branch equilibrium. These are supposed to help us determine ​ 
-good initial guesses for periodic orbits. Frankly, I don't get how, and I would like 
-some help understanding this. Chaosbook shows how to do with a few low-dimensional ​ 
-examples, by making a Poincare section, looking at the return map of the unstable manifold 
-on the section, and taking approximate fixed points of this map and its iterates as 
-initial guesses for orbits. But the examples, e.g. Rössler, have helpful properties that  
-are not present in plane Couette, namely insanely strong contraction along a 1-dimensional 
-stable direction. ​ 
- 
-So the question is, how can we find approximate fixed points of the return map when there 
-are ten or twenty directions of weaker contraction?​ 
- 
- 
-Suggested reading: 
- 
-   * [[gtspring2009:​gibson:​w03#​poincare_section|Gibson blog on poincare sections]]. ​ 
-   * [[http://​www.chaosbook.org/​chapters/​cycles.pdf]] 
- 
-===== Factoring out the 4th-order translation symmetry ===== 
gtspring2009/schedule/sections_orbits.txt · Last modified: 2010/02/02 07:55 (external edit)