Stefano Luzzatto

TL;DR: In this article, the authors study a class of geometric Lorenz flows, introduced independently by Afraimovic, Bykov & Sil'nikov and by Guckenheimer & Williams, and give a verifiable condition for such flows to be mixing.

TL;DR: In this article, the authors consider multimodal C3 interval maps f satisfying a summability condition on the derivatives Dn along the critical orbits which implies the existence of an absolutely continuous f-invariant probability measure mu.

TL;DR: In this article, the authors consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary dimension, possibly having discontinuities and/or critical sets, and show that under some general conditions they admit an induced Markov tower structure.

TL;DR: In this paper, the authors consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary dimension, possibly having discontinuities and/or critical sets, and show that under some general conditions they admit an induced Markov tower structure for which the decay of the return time function can be controlled in terms of the time generic points need to achieve some uniform expanding behavior.

TL;DR: In this paper, it was shown that in many cases stochastic-like behaviour itself implies that the system has certain non-trivial geometric properties, which are therefore necessary as well as sufficient conditions for the occurrence of the statistical properties under consideration.