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The 2-link periodic orbits which maximize or minimize the length of a p-dimensional Birkhoff billiard are hyperbolic

Marie-Claude Arnaud

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Recommended by L Bunimovich

We prove that in a p-dimensional billiard, every 2-link non-degenerate periodic solution which minimizes or maximizes the length is hyperbolic. This result generalizes the results of Treshchev concerning the case of the planar Birkhoff billiard.


PACS

05.45.-a Nonlinear dynamics and nonlinear dynamical systems

02.10.Yn Matrix theory

MSC

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

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 6 (November 2002)

Received 21 February 2002, in final form 15 July 2002

Published 9 September 2002



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