Polygonal symplectic billiards

Peter Albers; Gautam Banhatti; Filip Sadlo; Richard Evan Schwartz; Serge Tabachnikov

Polygonal symplectic billiards

Authors

Peter Albers Mathematisches Institut and Interdisciplinary Center for Scientific Computing https://orcid.org/0000-0002-7324-0609
Gautam Banhatti Ruhr-Universität Bochum https://orcid.org/0000-0002-8668-310X
Filip Sadlo Ruprecht-Karls-Universität Heidelberg https://orcid.org/0000-0002-8949-8452
Richard Evan Schwartz Brown University https://orcid.org/0000-0003-1383-2941
Serge Tabachnikov Pennsylvania State University https://orcid.org/0000-0001-5398-7820

Keywords:

Polygonal Symplectic Billiards

Abstract

In this article, we study polygonal symplectic billiards. We provide new results, some of which are inspired by numerical investigations. In particular, we present several polygons for which all orbits are periodic. We demonstrate their properties and derive various conjectures using two numerical implementations.

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Published

02/28/2025

How to Cite

Albers, P., Banhatti, G., Sadlo, F., Schwartz, R. E., & Tabachnikov, S. (2025). Polygonal symplectic billiards. Journal of Experimental Mathematics, 1(1), 1–22. Retrieved from https://jexpmath.org/index.php/jem/article/view/Vol-1Issue-1Paper-1