English

Integrable Billiards and Related Topics

Dynamical Systems 2025-10-21 v2 Differential Geometry

Abstract

This paper surveys our results on integrable billiards. We consider various models of billiards, including Birkhoff, outer, magnetic, and Minkowski billiards. Also, we discuss wire billiards and billiards in cones. For four models of convex plane billiards, we also discuss an isoperimetric-type inequality for the Mather β\beta-function. We conclude with a section of open questions on this subject.

Keywords

Cite

@article{arxiv.2510.03790,
  title  = {Integrable Billiards and Related Topics},
  author = {Misha Bialy and Andrey E. Mironov},
  journal= {arXiv preprint arXiv:2510.03790},
  year   = {2025}
}

Comments

Submitted to the proceedings of ICM 2026

R2 v1 2026-07-01T06:17:05.152Z