Dan Reznik’s identities and more

By Misha Bialy, Serge Tabachnikov. European Journal of Mathematics, 2020

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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.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/11fe16f16d64c1e41b6b53a7b2996965c0115928