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Bernoulli Property for Some Hyperbolic Billiards

Bernoulli Property for Some Hyperbolic Billiards We prove that hyperbolic billiards constructed by Bussolari and Lenci are Bernoullisystems. These billiards cannot be studied by existing approaches to analysis ofbilliards that have some focusing boundary components, which require the diameterof the billiard table to be of the same order as the largest curvature radiusalong the focusing component. Our proof employs a local ergodic theoremwhich states that, under certain conditions, there is a full measure setof the billiard phase space such that each point of the set has a neighborhoodcontained (mod 0) in a Bernoulli component of the billiard map. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Bernoulli Property for Some Hyperbolic Billiards

Regular and Chaotic Dynamics , Volume 25 (4) – Jul 30, 2020

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References (28)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2020
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354720040048
Publisher site
See Article on Publisher Site

Abstract

We prove that hyperbolic billiards constructed by Bussolari and Lenci are Bernoullisystems. These billiards cannot be studied by existing approaches to analysis ofbilliards that have some focusing boundary components, which require the diameterof the billiard table to be of the same order as the largest curvature radiusalong the focusing component. Our proof employs a local ergodic theoremwhich states that, under certain conditions, there is a full measure setof the billiard phase space such that each point of the set has a neighborhoodcontained (mod 0) in a Bernoulli component of the billiard map.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Jul 30, 2020

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