Non-robustly intermingled basins for perturbations of time-one map of Anosov flows

TL;DR

This paper investigates how small changes to the time-one map of transitive Anosov flows affect the structure of basins of hyperbolic physical measures, showing that most perturbations lack intermingled basins.

Contribution

It demonstrates that generic perturbations of these maps do not exhibit intermingled basins, clarifying the stability of hyperbolic measures under perturbations.

Findings

Most perturbations have no intermingled basins of hyperbolic physical measures.

Provides insight into the stability of dynamical structures under perturbations.

Enhances understanding of the robustness of Anosov flow properties.

Abstract

Perturbations of time-one maps of transitive Anosov flows are studied. We show that most perturbations have no intermingled basins of hyperbolic physical measures.