18 citations · 31 across the 7 of their papers we have counts for
Showing 2003 · math.DSShow all
3 papers · 2 filters
math.DS2003
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…
math.DS2003★ 1 cited
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…
math.DS2003★ 3 cited
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…