October 10, 2025Open Access

Integrable Billiards and Related Topics

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This survey presents various integrable billiard models, including magnetic billiards and Minkowski billiards, enriching the field with diverse perspectives.
Key findings involve a new isoperimetric-type inequality related to the Mather β-function for convex plane billiards, showcasing significant theoretical advancements.
The analysis covers specific models like wire billiards and billiards in cones, contributing to a broad understanding of integrable dynamics in these systems.
The conclusion raises open questions in integrable billiards, urging further exploration to deepen comprehension of the established concepts.

Implication

Survey highlights integrable billiards, including magnetic and Minkowski models, suggesting new inquiries.

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 $β$-function. We conclude with a section of open questions on this subject.

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Cite This Study

Bialy et al. (2025) studied this question.

synapsesocial.com/papers/68e865117ef2f04ca37e4e0c https://doi.org/10.48550/arxiv.2510.03790

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Implication

Survey highlights integrable billiards, including magnetic and Minkowski models, suggesting new inquiries.

Integrable Billiards and Related Topics

Key Points

Implication

Abstract

Discussion

Cite This Study

Integrable Billiards and Related Topics

Key Points

Implication

Abstract

Discussion

Cite This Study

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