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23 April 2024

» arxiv » 0910.2547

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Geometry of expanding absolutely continuous invariant measures and the liftability problem
Jose F. Alves ; Carla L. Dias ; Stefano Luzzatto ;
Date:	14 Oct 2009
Abstract:	We consider a quite broad class of maps on compact manifolds of arbitrary dimension possibly admitting critical points,discontinuities and singularities. Under some mild nondegeneracy assumptions we show that (f) admits an induced Gibbs-Markov map with integrable inducing times if and only if it has an ergodic invariant probability measure which is absolutely continuous with respect to the Riemannian volume and has all Lyapunov exponents positive.
Source:	arXiv, 0910.2547
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