Yet another induction scheme for non-uniformly expanding transformations

2017/02/28 by Capett-Figueras, Pedro L., Sánchez-Salas, Fernando J.
#37C40 #37D35 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.08878

Abstract

We introduce a new induction scheme for non-uniformly expanding maps f of compact Riemannian manifolds, proving that the existence of a Gibbs-Markov-Young structure is a necessary condition for f to preserve an absolutely continuous probability with all its Lyapunov exponents positive.

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