On the dominated splitting of Lyapunov stable aperiodic classes
Dynamical Systems
2015-06-26 v1
Abstract
Recent works related to Palis conjecture of J. Yang, S. Crovisier, M. Sambarino and D. Yang showed that any aperiodic class of a -generic diffeomorphism far away from homoclinic bifurcations (or homoclinic tangencies) is partially hyperbolic. We show in this paper that, generically, a non-trivial dominated splitting implies partial hyperbolicity for an aperiodic class if it is Lyapunov stable. More precisely, for -generic diffeomorphisms, if a Lyapunov stable aperiodic class has a non-trivial dominated splitting , then one of the two bundles is hyperbolic (either is contracted or is expanded).
Keywords
Cite
@article{arxiv.1506.07784,
title = {On the dominated splitting of Lyapunov stable aperiodic classes},
author = {Xiaodong Wang},
journal= {arXiv preprint arXiv:1506.07784},
year = {2015}
}