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Scaling rate for semi-dispersing billiards with non-compact cusps

Published online by Cambridge University Press:  08 November 2011

A. ARBIETO ,
R. MARKARIAN ,
M. J. PACIFICO  and
R. SOARES
A. ARBIETO
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil (email: arbieto@im.ufrj.br, pacifico@im.ufrj.br)
R. MARKARIAN
Affiliation:
Instituto de Matemática y Estadística (IMERL), Facultad de Ingeniería, Universidad de la República, CC30, CP 11300, Montevideo, Uruguay (email: roma@fing.edu.uy)
M. J. PACIFICO
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil (email: arbieto@im.ufrj.br, pacifico@im.ufrj.br)
R. SOARES
Affiliation:
Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, Brazil (email: regis.soares@ufjf.edu.br)
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Abstract

We show that certain billiard tables with non-compact cusps are mixing with respect to the invariant infinite measure, in the sense of Krengel and Sucheston. Moreover, we show that the scaling rate is slower than a certain polynomial rate.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 6 , December 2012 , pp. 1836 - 1861
Copyright
Copyright © Cambridge University Press 2011

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