Dan Reznik's identities and more
Differential Geometry
2020-05-06 v2 Dynamical Systems
Abstract
Dan Reznik found, by computer experimentation, a number of conserved quantities associated with periodic billiard trajectories in ellipses. We prove some of his observations using a non-standard generating function for the billiard ball map. In this way, we also obtain some identities valid for all smooth convex billiard tables.
Keywords
Cite
@article{arxiv.2001.08469,
title = {Dan Reznik's identities and more},
author = {Misha Bialy and Serge Tabachnikov},
journal= {arXiv preprint arXiv:2001.08469},
year = {2020}
}
Comments
This is an extended version