Yet another induction scheme for non-uniformly expanding transformations

Pedro L. Capett-Figueras, Fernando J. Sánchez-Salas

Published 2017-02-28Version 1

We introduce a new induction scheme for non-uniformly expanding maps $f$ of compact Riemannian manifolds, relying upon ideas of S\'anchez-Salas and Neil Doobs, 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.