Weak mixing in rational billiards

Fuente: arXiv
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Auteurs principaux: Arana-Herrera, Francisco, Chaika, Jon, Forni, Giovanni
Format: Preprint
Publié: 2024
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author Arana-Herrera, Francisco
Chaika, Jon
Forni, Giovanni
author_facet Arana-Herrera, Francisco
Chaika, Jon
Forni, Giovanni
contents We completely characterize rational polygons whose billiard flow is weakly mixing in almost every direction as those which are not almost integrable, in the terminology of Gutkin, modulo some low complexity exceptions. This proves a longstanding conjecture of Gutkin. This result is derived from a complete characterization of translation surfaces that are weakly mixing in almost every direction: they are those that do not admit an affine factor map to the circle.
format Preprint
id arxiv_https___arxiv_org_abs_2410_11117
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Weak mixing in rational billiards
Arana-Herrera, Francisco
Chaika, Jon
Forni, Giovanni
Dynamical Systems
37A25, 37C83, 37E35. 37F34
We completely characterize rational polygons whose billiard flow is weakly mixing in almost every direction as those which are not almost integrable, in the terminology of Gutkin, modulo some low complexity exceptions. This proves a longstanding conjecture of Gutkin. This result is derived from a complete characterization of translation surfaces that are weakly mixing in almost every direction: they are those that do not admit an affine factor map to the circle.
title Weak mixing in rational billiards
topic Dynamical Systems
37A25, 37C83, 37E35. 37F34
url https://arxiv.org/abs/2410.11117