18 citations · 31 across the 7 of their papers we have counts for
7 papers · 1 filter
Topological invariance of the sign of the Lyapunov exponents in one-dimensional maps
Henk Bruin, Stefano Luzzatto
We explore some properties of Lyapunov exponents of measures preserved by smooth maps of the interval, and study the behaviour of the Lyapunov exponents under topological conjugacy…
Stochastic-like behaviour in nonuniformly expanding maps
Stefano Luzzatto
This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss…
A minimum principle for Lyapunov exponents and a higher-dimensional version of a Theorem of Mane'
Yongluo Cao, Stefano Luzzatto, Isabel Rios
We consider compact invariant sets Λfor C^{1} maps in arbitrary dimension. We prove that if Λcontains no critical points then there exists an invariant probability measure with a L…
Some non-hyperbolic systems with strictly non-zero Lyapunov exponents for all invariant measures: Horseshoes with internal tangencies
Yongluo Cao, Stefano Luzzatto, Isabel Rios
We study the hyperbolicity of a class of horseshoes exhibiting an internal tangency, i.e. a point of homoclinic tangency accumulated by periodic points. In particular these systems…
Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results
Stefano Luzzatto
We discuss recent results on decay of correlations for non-uniformly expanding maps. Throughout the discussion, we address the question of why different dynamical systems have diff…
Decay of correlations in one-dimensional dynamics
Henk Bruin, Stefano Luzzatto, Sebastian van Strien
We consider multimodal C^3 interval maps f satisfying a summability condition on the derivatives D_n along the critical orbits which implies the existence of an absolutely continuo…