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Yet another induction scheme for non-uniformly expanding transformations

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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… Click to show full 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.

Keywords: induction scheme; non uniformly; scheme non; uniformly expanding

Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018

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