Finitely many physical measures for sectional-hyperbolic attracting sets and statistical stability
Dynamical Systems
2021-09-07 v2
Abstract
We show that a sectional-hyperbolic attracting set for a H\"older- vector field admits finitely many physical/SRB measures whose ergodic basins cover Lebesgue almost all points of the basin of topological attraction. In addition, these physical measures depend continuously on the flow in the topology, that is, sectional-hyperbolic attracting sets are statistically stable. To prove these results we show that each central-unstable disk in a neighborhood of this class of attracting sets is eventually expanded to contain a ball whose inner radius is uniformly bounded away from zero.
Cite
@article{arxiv.1901.10537,
title = {Finitely many physical measures for sectional-hyperbolic attracting sets and statistical stability},
author = {Vitor Araujo},
journal= {arXiv preprint arXiv:1901.10537},
year = {2021}
}
Comments
27 pages; 2 figures. Improved statements and proofs after referee comments; version accepted to appear in Ergodic Theory and Dynamical Systems