gtspring2009:schedule:sections_orbits
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gtspring2009:schedule:sections_orbits [2009/04/10 08:11] gibson |
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| - | ====== April 14 study group ====== | ||
| - | Some topics I would like to discuss. Feel free to add your own. //John Gibson 2009-04-10 11:11 EST// | ||
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| - | ===== Poincare sections and periodic orbits ===== | ||
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| - | 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. | ||
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| - | 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? | ||
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| - | Suggested reading: | ||
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| - | * [[gtspring2009:gibson:w03#poincare_section|Gibson blog on poincare sections]]. | ||
| - | * [[http://www.chaosbook.org/chapters/cycles.pdf]] | ||
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| - | ===== Factoring out the 4th-order translation symmetry ===== | ||
gtspring2009/schedule/sections_orbits.txt · Last modified: 2010/02/02 07:55 (external edit)
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