Semi-focusing billiards : Hyperbolicity

In this paper we answer affirmatively the question concerning the existence of hyperbolic billiards in convex domains of ℝ3. We also prove that a related class of semi-focusing billiards has mixed dynamics, i.e., their phase space is an union of two invariant sets of positive measure such that the d...

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Bibliographic Details
Published in:	Communications in mathematical physics Vol. 262; no. 1; pp. 17 - 32
Main Authors:	BUNIMOVICH, Leonid A, DEL MAGNO, Gianluigi
Format:	Journal Article
Language:	English
Published:	Heidelberg Springer 01-02-2006 Springer Nature B.V
Subjects:	Billiards Domains Exact sciences and technology Global analysis, analysis on manifolds Mathematics Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Invariant set Dynamical system Phase space Focusing Mathematical physics
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Summary:	In this paper we answer affirmatively the question concerning the existence of hyperbolic billiards in convex domains of ℝ3. We also prove that a related class of semi-focusing billiards has mixed dynamics, i.e., their phase space is an union of two invariant sets of positive measure such that the dynamics is integrable on one set and is hyperbolic on the other. These billiards are the first rigorous examples of billiards in domains of ℝ3 with divided phase space.
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-005-1473-8