Timeline for Are periodic billiard trajectories stable on a manifold with strictly convex boundary?
Current License: CC BY-SA 3.0
5 events
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| Jul 28, 2015 at 15:51 | history | edited | user25199 | CC BY-SA 3.0 |
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| Jul 28, 2015 at 15:43 | history | edited | user25199 | CC BY-SA 3.0 |
added 580 characters in body
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| Jul 28, 2015 at 13:50 | comment | added | user25199 | According to the usual variational principle, periodic orbits are stationary points of the total length of the orbit according to the metric, fixing the $n$ points on the boundary. Generic smooth functions in a compact space have only a finite number of critical points. | |
| Jul 28, 2015 at 13:20 | comment | added | Joonas Ilmavirta | Why do you expect to have a finite number of periodic orbits for a fixed number of reflections in a generic metric? This is not true if the metric is radially symmetric, but radial symmetry is admittedly not a generic property. Sounds plausible, but I don't see a simple argument. | |
| Jul 28, 2015 at 12:08 | history | answered | user25199 | CC BY-SA 3.0 |