Half circle dual billiard
We look a bit at the beautiful problem of dual billiards=exterior billiards = cobilliard=Moser billiard. It is known since 2009 that the half circle dual billiard has orbits going to infinity. No C^1 table is known which produces instability. I look here at the orbit of (2,1) where the growth rate is pretty sharp (3/4) sqrt(n) . Unstable orbits of the half circle billiard were first observed by Serge Tabatchnikov in 1996. It was a rainy day today. Was only flying around inside.
Some links: (to my own stuff. General things can be found by googling. Our department stuff can hardly be fond on google, mainly due to server name changes).
• Math E 320 Spring 2021 Ten Dynamical systems my 10 most favorite dynamical systems, the fifth one is exterior billiard (Youtube from April 18, 2021 for Math E 320)
- • Top ten chaotic dynamical systems a short version of the top 10 chaotic systems
(Youtube from April 18, 2022 for Math E 320)
page 89 in Moser's "Selected Topics in the Calculus of variations" (2003 script by O. Knill)
https://people.math.harvard.edu/~knil...
A handout from Harvard Math 118r taught in the spring semester of 2005:
https://people.math.harvard.edu/archi...
Mathematik.com Exterior billiards https://mathematik.com/Exterior/index...
a page from 2005
A math circle talk from February 11, 2003 (Bob and Ellen Kaplan's venture)
https://people.math.harvard.edu/~knil...