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Absolutely continuous invariant measures for non-uniformly expanding maps

Published online by Cambridge University Press:  01 August 2009

HUYI HU  and
SANDRO VAIENTI
HUYI HU
Affiliation:
Mathematics Department, Michigan State University, East Lansing, MI 48824, USA (email: hu@math.msu.edu)
SANDRO VAIENTI
Affiliation:
UMR-6207 Centre de Physique Théorique, CNRS, Universités d’Aix-Marseille I, II, Université du Sud Toulon-Var and FRUMAM, Fédéderation de Recherche des Unitiés de Mathématiques de Marseille, France (email: vaienti@cpt.univ-mrs.fr)
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Abstract

For a large class of non-uniformly expanding maps of ℝm, with indifferent fixed points and unbounded distortion and that are non-necessarily Markovian, we construct an absolutely continuous invariant measure. We extend previously used techniques for expanding maps on quasi-Hölder spaces to our case. We give general conditions and provide examples to which our results apply.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 4 , August 2009 , pp. 1185 - 1215
Copyright
Copyright © Cambridge University Press 2009

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