Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Fan, Wentao, Hasselblatt, Boris
Institution: Hebei Normal University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223034797