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PreprintCC BY 4.0arXiv

Strictly convex ergodic billiards

  • Wentao Fan
  • Boris Hasselblatt
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Abstract

We produce the first known strictly convex ergodic billiards: sufficiently asymmetric lemon billiards. These billiard tables are the intersection of two circles of which one contains the centers of both. We previously proved that they have \emph{uniformly} hyperbolic returns to a suitable section, and we here control singularity curves, with an approach that seems new. This implies ergodicity and indeed the Bernoulli property.

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Cite

BibTeXRIS
BibTeX
@misc{fan2026strictly,
  title = {{Strictly convex ergodic billiards}},
  author = {Wentao Fan and Boris Hasselblatt},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28247},
  eprint = {2610.28247},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28247},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Strictly convex ergodic billiards
AU  - Wentao Fan
AU  - Boris Hasselblatt
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28247
UR  - https://arxiv.org/abs/2610.28247
AB  - We produce the first known strictly convex ergodic billiards: sufficiently asymmetric lemon billiards. These billiard tables are the intersection of two circles of which one contains the centers of both. We previously proved that they have \emph{uniformly} hyperbolic returns to a suitable section, and we here control singularity curves, with an approach that seems new. This implies ergodicity and indeed the Bernoulli property.
ER  -