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Absolutely continuous invariant measures for piecewise expanding C2 transformations in Rn on domains with cusps on the boundaries

Published online by Cambridge University Press:  19 September 2008

Kourosh Adl-Zarabi
Kourosh Adl-Zarabi
Affiliation:
Department of Mathematics and Statistics, Concordia University, 7141 Sherbrooke St West, Montreal, CanadaH4B 1R6 (email: zarabi@vax2.concordia.ca)
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Abstract

Let Ω be a bounded region in Rn and let be a partition of Ω into a finite number of subsets having piecewise C2 boundaries. The boundaries may contain cusps. Let τ: Ω → Ω be piecewise C2 on and expanding in the sense that there exists α > 1 such that for any i = 1, 2,…,m, where is the derivative matrix of and ‖·‖ is the euclidean matrix norm. The main result provides a lower bound on α which guarantees the existence of an absolutely continuous invariant measure for τ.

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 1 , February 1996, pp. 1 - 18
Copyright
Copyright © Cambridge University Press 1996

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