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Billiards with polynomial decay of correlations

Published online by Cambridge University Press:  02 February 2004

ROBERTO MARKARIAN
ROBERTO MARKARIAN
Affiliation:
Instituto de Matem´tica y Estadística ‘Prof. Ing. Rafael Laguardia’, Facultad de Ingeniería, Universidad de la República, C.C. 30, Montevideo, Uruguay (e-mail: [email protected])
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Abstract

We prove that the billiard map in a Bunimovich stadium has polynomial decay of correlations of the order of n-1. Ergodic Bunimovich-type billiards (two arcs not bigger than half a circle) that do not have trajectories with infinitely many consecutive bounces on straight lines satisfy the same property. We also prove that a very particular class of these billiards have polynomial decay of correlations of the order of n-2.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 1 , February 2004 , pp. 177 - 197
Copyright
2004 Cambridge University Press

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