Integrable Billiards and Related Topics

Integrable Billiards and Related Topics Full article

Conference

International Congress of Mathematicians 2026
23-30 Jul 2026 , New York City

Source

Proceedings of the International Congress of Mathematicians 2026. Invited Lectures (Sections 9–11)
Compilation, 2026.

Output data

Year: 2026, Volume: 5, Pages: 42-58 Pages count : 17 DOI: 10.1137/25m1804078

Tags

integrable billiards, Birkhoff--Poritsky conjecture, monotone twist maps, invariant curves

Authors

Bialy Misha ¹ , Mironov Andrey E. ^2,3

Affiliations

1	School of Mathematical Sciences, Tel Aviv University, Israel
2	Sobolev Institute of Mathematics and Novosibirsk State University, Russia
3	Sobolev Institute of Mathematics

Funding (1)

Министерство науки и высшего образования РФ

FWNF-2026-0026

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 incones. For four models of convex plane billiards, we also discuss an isoperimetric-type inequality for the Mather\beta -function. We conclude with a section of open questions on this subject.

Bialy M. , Mironov A.E.
Integrable Billiards and Related Topics
In compilation Proceedings of the International Congress of Mathematicians 2026. Invited Lectures (Sections 9–11). 2026. – Т.5. – C.42-58. DOI: 10.1137/25m1804078 OpenAlex

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