Intersection of stable and unstable manifolds for invariant Morse functions

TL;DR

This paper investigates the geometric structure of the intersection between stable and unstable manifolds in the context of invariant Morse-Smale functions, providing insights into their manifold properties.

Contribution

It offers a detailed analysis of the intersection structure of stable and unstable manifolds for invariant Morse-Smale functions, a topic not extensively explored before.

Findings

Characterization of the intersection as a smooth manifold

Conditions under which the intersection is non-empty and well-behaved

Insights into the topology of the intersection manifold

Abstract

We study the structure of the smooth manifold which is defined as the intersection of a stable manifold and an unstable manifold for an invariant Morse-Smale function.