Homoclinic classes for sectional-hyperbolic sets

TL;DR

This paper proves that all Lyapunov stable sets with sectional-hyperbolic structure necessarily contain nontrivial homoclinic classes, advancing understanding of the dynamics within such sets.

Contribution

It establishes a fundamental link between sectional-hyperbolic Lyapunov stable sets and the existence of homoclinic classes, a novel result in dynamical systems theory.

Findings

Every sectional-hyperbolic Lyapunov stable set contains a nontrivial homoclinic class.

Provides new insights into the structure of stable sets in dynamical systems.

Enhances understanding of the relationship between hyperbolic structures and homoclinic phenomena.

Abstract

We prove that every sectional-hyperbolic Lyapunov stable set contains a nontrivial homoclinic class.