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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
Affiliation:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil (email: [email protected], [email protected])
R. MARKARIAN
Affiliation:
Instituto de Matemática y Estadística (IMERL), Facultad de Ingeniería, Universidad de la República, CC30, CP 11300, Montevideo, Uruguay (email: [email protected])
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: [email protected], [email protected])
R. SOARES
Affiliation:
Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Juiz de Fora, Juiz de Fora, MG, Brazil (email: [email protected])

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
Copyright
Copyright © Cambridge University Press 2011

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