Effective rigidity away from the boundary for centrally symmetric billiards

Misha Bialy

doi:10.1017/etds.2023.70

Effective rigidity away from the boundary for centrally symmetric billiards

Misha Bialy

School of Mathematical Sciences

Tel Aviv University

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

Abstract

In this paper, we study centrally symmetric Birkhoff billiard tables. We introduce a closed invariant set consisting of locally maximizing orbits of the billiard map lying inside the region bounded by two invariant curves of -periodic orbits. We give an effective bound from above on the measure of this invariant set in terms of the isoperimetric defect of the curve. The equality case occurs if and only if the curve is a circle.

Original language	English
Pages (from-to)	1741-1756
Number of pages	16
Journal	Ergodic Theory and Dynamical Systems
Volume	44
Issue number	7
DOIs	https://doi.org/10.1017/etds.2023.70
State	Published - 1 Jul 2024

Keywords

integrable billiards
minimal action
rigidity

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1017/etds.2023.70

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abstract = "In this paper, we study centrally symmetric Birkhoff billiard tables. We introduce a closed invariant set consisting of locally maximizing orbits of the billiard map lying inside the region bounded by two invariant curves of -periodic orbits. We give an effective bound from above on the measure of this invariant set in terms of the isoperimetric defect of the curve. The equality case occurs if and only if the curve is a circle.",

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N2 - In this paper, we study centrally symmetric Birkhoff billiard tables. We introduce a closed invariant set consisting of locally maximizing orbits of the billiard map lying inside the region bounded by two invariant curves of -periodic orbits. We give an effective bound from above on the measure of this invariant set in terms of the isoperimetric defect of the curve. The equality case occurs if and only if the curve is a circle.

AB - In this paper, we study centrally symmetric Birkhoff billiard tables. We introduce a closed invariant set consisting of locally maximizing orbits of the billiard map lying inside the region bounded by two invariant curves of -periodic orbits. We give an effective bound from above on the measure of this invariant set in terms of the isoperimetric defect of the curve. The equality case occurs if and only if the curve is a circle.

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KW - minimal action

KW - rigidity

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Effective rigidity away from the boundary for centrally symmetric billiards

Abstract

Keywords

ASJC Scopus subject areas

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