NDLI: On the Bernoulli Property of Planar Hyperbolic Billiards

Content Provider	Springer Nature Link
Author	Del Mag, Gianluigi Markarian, Roberto
Copyright Year	2017
Abstract	We consider billiards in non-polygonal domains of the plane with boundary consisting of curves of three different types: straight segments, strictly convex inward curves and strictly convex outward curves of a special kind. The billiard map for these domains is known to have non-vanishing Lyapunov exponents a.e. provided that the distance between the curved components of the boundary is sufficiently large, and the set of orbits having collisions only with the flat part of the boundary has zero measure. Under a few additional conditions, we prove that there exists a full measure set of the billiard phase space such that each of its points has a neighborhood contained up to a zero measure set in one Bernoulli component of the billiard map. Using this result, we show that there exists a large class of planar hyperbolic billiards that have the Bernoulli property. This class includes the billiards in convex domains bounded by straight segments and strictly convex inward arcs constructed by Donnay.
Starting Page	917
Ending Page	955
Page Count	39
File Format	PDF
ISSN	00103616
Journal	Communications in Mathematical Physics
Volume Number	350
Issue Number	3
e-ISSN	14320916
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2017-01-25
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Mathematical Physics Quantum Physics Complex Systems Classical and Quantum Gravitation, Relativity Theory
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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