Robust criterion for the existence of nonhyperbolic ergodic measures
Abstract
We give explicit -open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with one-dimensional center and positive topological entropy on which the center Lyapunov exponent vanishes uniformly. The conditions of the criterion are met on a -dense and open subset of the set of a diffeomorphisms having a robust cycle. As a corollary, there exists a -open and dense subset of the set of non-Anosov robustly transitive diffeomorphisms consisting of systems with nonhyperbolic ergodic measures with positive entropy. The criterion is based on a notion of a blender defined dynamically in terms of strict invariance of a family of discs.
Cite
@article{arxiv.1502.06535,
title = {Robust criterion for the existence of nonhyperbolic ergodic measures},
author = {Jairo Bochi and Christian Bonatti and Lorenzo J. Díaz},
journal= {arXiv preprint arXiv:1502.06535},
year = {2016}
}