Christian Foltin 2002 Nonlinearity 15 2053 doi:10.1088/0951-7715/15/6/314
Christian Foltin
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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.
37C27 Periodic orbits of vector fields and flows
37B10 Symbolic dynamics (See also 37Cxx, 37Dxx)
37D50 Hyperbolic systems with singularities (billiards, etc.)
Issue 6 (November 2002)
Received 31 July 2001, in final form 6 September 2002
Published 14 October 2002
Christian Foltin 2002 Nonlinearity 15 2053
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