Dan Reznik’s identities and more

Misha Bialy; Serge Tabachnikov

doi:10.1007/s40879-020-00428-7

Dan Reznik’s identities and more

Misha Bialy, Serge Tabachnikov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1341-1354
Number of pages	14
Journal	European Journal of Mathematics
Volume	8
Issue number	4
DOIs	https://doi.org/10.1007/s40879-020-00428-7
State	Published - Dec 2022

Keywords

Conservation laws
Generating function
Planar billiard

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/s40879-020-00428-7

Cite this

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title = "Dan Reznik{\textquoteright}s identities and more",

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.",

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doi = "10.1007/s40879-020-00428-7",

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AB - 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.

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Dan Reznik’s identities and more

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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