Physical Measures for Partially Hyperbolic Surface Endomorphisms

Hyperbolic Saddle Measures and Laminarity for Holomorphic Endomorphisms of P2c

We study the laminarity of the Green current of endomorphisms of P2(C) near hyperbolic measures of saddle type. When these measures are supported by attracting sets, we prove that the Green current is laminar in the basin of attraction and we obtain new ergodic properties. This generalizes some results of Bedford and Jonsson on regular polynomial mappings in C2.

Pointwise Dimension for Regular Hyperbolic Measures for Endomorphisms

A Multifractal Analysis of Gibbs Measures for Conformal Expanding Maps and Markov Moran Geometric Constructions

We establish the complete multifractal formalism for Gibbs measures for confor-mal expanding maps and Markov Moran geometric constructions. Examples include Markov maps of an interval, hyperbolic Julia sets, and conformal toral endomorphisms. This paper describes the multifractal analysis of measures invariant under dynamical systems. The concept of a multifractal analysis was suggested by seve...

Existence and convergence results for monotone nonexpansive type mappings in‎ ‎partially ordered hyperbolic metric spaces

‎We present some existence and convergence results for a general class of nonexpansive mappings in partially ordered hyperbolic metric spaces‎. ‎We also give some examples to show the generality of the mappings considered herein.

On the Topologically Conjugate Classes of Anosov Endomorphisms on Tori

This paper considers the following question: Given an Anosov endomorphism f on T, whether f is topologically conjugate to some hyperbolic toral endomorphism? It is well known that the answer for Anosov diffeomorphisms and expanding endomorphisms is affirmative. However, for the remainder Anosov endomorphisms, a quite different answer is obtained in this paper, i.e., for generic Anosov endomorph...