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Billiards with positive topological entropy

Christian Foltin

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Recommended by L Bunimovich

We prove that billiard flows on strictly convex tables with a sufficiently small circular scatterer generically admit positive topological entropy. In particular, we show that billiard systems in non-concentric circular annuli have the same property for sufficiently small inner radii in both Euclidean and hyperbolic spaces. Moreover the number of orbits which join two given outer configuration points in less than n iterations of the billiard map increases exponentially fast in n.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

02.40.-k Geometry, differential geometry, and topology

MSC

37C27 Periodic orbits of vector fields and flows

37B10 Symbolic dynamics (See also 37Cxx, 37Dxx)

37C35 Orbit growth

37D50 Hyperbolic systems with singularities (billiards, etc.)

37B40 Topological entropy

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 6 (November 2002)

Received 31 July 2001, in final form 6 September 2002

Published 14 October 2002



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