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On the liftability of expanding stationary measures
Stochastics and Dynamics  (IF0.98),  Pub Date : 2021-01-07, DOI: 10.1142/s0219493721500398
José F. Alves, Carla L. Dias, Helder Vilarinho

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.