PreprintCC0arXiv
Uniformly hyperbolic strictly convex billiards
Abstract
Can a strictly convex billiard be ergodic? For the billiard in a suitable intersection of two circles, we establish \emph{uniform} expansion of vectors in an invariant cone family under the return to a well-chosen section. This is the first and most onerous step towards a forthcoming proof of ergodicity (the Chen--Mohr--Zhang--Zhang conjecture) and statistical properties. Together, this appears to be the first time that a strictly convex billiard is shown to be ergodic.
Related
- Strictly convex ergodic billiards
- Unbounded orbits in C1-generic centrally symmetric strictly convex outer billiards
- Strictly stable solutions in uniformly convex planar domains may have nonconvex superlevel sets
- Level set estimates for strictly convex and hyperbolic functions
- Dynamics of planar integrable Kepler billiards with a focused hyperbolic branch
BibTeX
@misc{fan2026uniformly,
title = {{Uniformly hyperbolic strictly convex billiards}},
author = {Wentao Fan and Boris Hasselblatt},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26441},
eprint = {2610.26441},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26441},
note = {CC0},
}
RIS
TY - UNPB
TI - Uniformly hyperbolic strictly convex billiards
AU - Wentao Fan
AU - Boris Hasselblatt
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26441
UR - https://arxiv.org/abs/2610.26441
AB - Can a strictly convex billiard be ergodic? For the billiard in a suitable intersection of two circles, we establish \emph{uniform} expansion of vectors in an invariant cone family under the return to a well-chosen section. This is the first and most onerous step towards a forthcoming proof of ergodicity (the Chen--Mohr--Zhang--Zhang conjecture) and statistical properties. Together, this appears to be the first time that a strictly convex billiard is shown to be ergodic.
ER -