Homoclinic classes for flows: ergodicity and SRB measures
Dynamical Systems
2025-12-04 v2
Abstract
In this work we intend to study homoclinic classes for some classes of flows. To this end we obtain analogous results those obtained by Hertz-Hertz-Tahzibi-Ures in the flow setting. Namely we prove that if the Lesbegue measure gives positive measure to both stable and unstable homoclinic classes of a periodic hyperbolic orbit, then their intersection constitute an ergodic component. Futhermore, with similar techiniques we state several results concerning regular SRB measures.
Keywords
Cite
@article{arxiv.2502.12260,
title = {Homoclinic classes for flows: ergodicity and SRB measures},
author = {Ygor de Jesus and Marcielis Espitia and Gabriel Ponce},
journal= {arXiv preprint arXiv:2502.12260},
year = {2025}
}
Comments
20 pages, 4 figures