Effective rigidity away from the boundary for centrally symmetric billiards

Misha Bialy*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we study centrally symmetric Birkhoff billiard tables. We introduce a closed invariant set MB consisting of locally maximizing orbits of the billiard map lying inside the region B bounded by two invariant curves of 4-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 languageEnglish
JournalErgodic Theory and Dynamical Systems
StateAccepted/In press - 2023


FundersFunder number
Deutsche ForschungsgemeinschaftMA-2565/7-1
Israel Science Foundation580/20


    • integrable billiards
    • minimal action
    • rigidity


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