Statistical stability for diffeomorphisms with mostly expanding and mostly contracting centers
Dynamical Systems
2020-03-11 v1
Abstract
For partially hyperbolic diffeomorphisms with mostly expanding and mostly contracting centers, we establish a topological structure, called skeleton{a set consisting of finitely many hyperbolic periodic points with maximal cardinality for which there exist no heteroclinic intersections. We build the one-to-one corresponding between periodic points in any skeleton and physical measures. By making perturbations on skeletons, we study the continuity of physical measures with respect to dynamics under -topology.
Cite
@article{arxiv.2003.04512,
title = {Statistical stability for diffeomorphisms with mostly expanding and mostly contracting centers},
author = {Zeya Mi and Yongluo Cao},
journal= {arXiv preprint arXiv:2003.04512},
year = {2020}
}