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arXiv · 1904.13343

On the liftability of expanding stationary measures

Jose F. Alves·Carla L. Dias·Helder Vilarinho
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Abstract

We consider random perturbations of a topologically transitive local diffeomorphism of a Riemannian manifold. We show that if an absolutely continuous ergodic stationary measures is expanding (all Lyapunov exponents positive), then there is a random Gibbs-Markov-Young structure which can be used to lift that measure. We also prove that if the original map admits a finite number of expanding invariant measures then the stationary measures of a sufficiently small stochastic perturbation are expanding.

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Jose F. Alves, Carla L. Dias, Helder Vilarinho. 2019-04-30. On the liftability of expanding stationary measures. https://arxiv.org/abs/1904.13343

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