Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes
Dynamical Systems
2015-07-30 v1
Abstract
We prove that, for -generic diffeomorphisms, if a homoclinic class is not hyperbolic, then there is a non-hyperbolic ergodic measure supported on it. This proves a conjecture by D\'iaz and Gorodetski [28]. We also discuss the conjectured existence of periodic points with different stable dimension in the class.
Cite
@article{arxiv.1507.08253,
title = {Hyperbolicity versus non-hyperbolic ergodic measures inside homoclinic classes},
author = {Cheng Cheng and Sylvain Crovisier and Shaobo Gan and Xiaodong Wang and Dawei Yang},
journal= {arXiv preprint arXiv:1507.08253},
year = {2015}
}