arXiv subjects

S. Luzzatto

Publications and source records attributed to S. Luzzatto.

3 recordsLinked to original sources

arXiv2014

SRB measures for partially hyperbolic systems whose central direction is weakly expanding

We consider partially hyperbolic \( C^{1+} \) diffeomorphisms of compact Riemannian manifolds of arbitrary dimension which admit a partially hyperbolic tangent bundle decomposition \( E^s\oplus E^{cu} \). Assuming the existence of a set of positive Lebesgue measure on which \( f \) satisfies a weak nonuniform expansivity assumption in the centre~unstable direction, we prove that there exists at most a finite number of transitive attractors each of which supports an SRB measure. As part of our argument, we prove that each attractor admits a Gibbs-Markov-Young geometric structure with integrable return times. We also characterize in this setting SRB measures which are liftable to Gibbs-Markov-Young structures.

math.DS↗

arXiv2007

Statistical properties of one-dimensional maps with critical points and singularities

We prove that a class of one-dimensional maps with an arbitrary number of non-degenerate critical and singular points admits an induced Markov tower with exponential return time asymptotics. In particular the map has an absolutely continuous invariant probability measure with exponential decay of correlations for Hölder observations.

math.DS↗

arXiv2002

Markov structures and decay of correlations for non-uniformly expanding dynamical systems

We 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. As a consequence we obtain some rates for the decay of correlations of those maps and conditions for the validity of the Central Limit Theorem.

math.DS↗