TY - JOUR
T1 - Effective rigidity away from the boundary for centrally symmetric billiards
AU - Bialy, Misha
N1 - Publisher Copyright:
© The Author(s), 2023.
PY - 2024/7/1
Y1 - 2024/7/1
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.
KW - integrable billiards
KW - minimal action
KW - rigidity
UR - https://www.scopus.com/pages/publications/85173757712
U2 - 10.1017/etds.2023.70
DO - 10.1017/etds.2023.70
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85173757712
SN - 0143-3857
VL - 44
SP - 1741
EP - 1756
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 7
ER -