Stochastic stability at the boundary of expanding maps

2004/04/20 by Vitor Araujo, Ali Tahzibi
Mathematics · #math.DS #msc:37D25 #msc:37D30 #msc:37D20

paper · pdf · doi:10.1088/0951-7715/18/3/001

published as Nonlinearity, 18 (2005) 1-20.

arxiv created 2004/04/20 · arxiv updated 2009/12/01

Abstract

We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit measures for a model of the intermittent map and obtain stochastic stability for some values of the parameter. The physical measures are obtained as zero-noise limits which are shown to satisfy Pesin?s Entropy Formula.

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