Discrete and Continuous Dynamical Systems, Volume (38), No (4), Year (2017-12) , Pages (1-31)

Title : ( Physical measures for certain class of non-uniformly hyperbolic endomorphisms on the solid torus )

Authors: marzie zaj , Fateme Helen Ghane Ostadghassemi , Azam Ehsani , A. Fakhari ,

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Abstract

In this paper we address the existence and ergodicity of non-uniformly hyperbolic attracting sets for a certain class of smooth endomorphisms on the solid torus. Such systems have formulation as a skew product system defined by planar diffeomorphisms, with average contraction condition, forced by any expanding circle map. These attractors are invariant graphs of upper semicontinuous maps which support exactly one physical measure. In our approach, these skew product systems arising from iterated function systems which are generated by finitely many weak contractive diffeomorphisms. Under some conditions including negative fiber Lyapunov exponents, we prove the existence of unique non-uniformly hyperbolic attracting invariant graphs for these systems which attract positive orbits of almost all initial points. Also, we prove that these systems are Bernoulli and therefore they are mixing. Moreover, these properties remain true under small perturbations in the space of endomorphisms on the solid torus.

Keywords

, Skew products, attractors, invariant graph, ergodic measure, physical measure, iterated function systems.
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@article{paperid:1066221,
author = {Zaj, Marzie and Ghane Ostadghassemi, Fateme Helen and Ehsani, Azam and A. Fakhari},
title = {Physical measures for certain class of non-uniformly hyperbolic endomorphisms on the solid torus},
journal = {Discrete and Continuous Dynamical Systems},
year = {2017},
volume = {38},
number = {4},
month = {December},
issn = {1078-0947},
pages = {1--31},
numpages = {30},
keywords = {Skew products; attractors; invariant graph; ergodic measure; physical measure; iterated function systems.},
}

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%0 Journal Article
%T Physical measures for certain class of non-uniformly hyperbolic endomorphisms on the solid torus
%A Zaj, Marzie
%A Ghane Ostadghassemi, Fateme Helen
%A Ehsani, Azam
%A A. Fakhari
%J Discrete and Continuous Dynamical Systems
%@ 1078-0947
%D 2017

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