Dan Reznik's identities and more
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Publication:6333366
DOI10.1007/S40879-020-00428-7zbMATH Open1509.37070arXiv2001.08469MaRDI QIDQ6333366
Misha Bialy, Sergei Tabachnikov
Publication date: 23 January 2020
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.
Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Geometric constructions in real or complex geometry (51M15) Dynamical systems with singularities (billiards, etc.) (37C83)
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