# Lipschitz perturbations of Morse-Smale semigroups

## TL;DR

This paper investigates how Lipschitz continuous, non-differentiable perturbations affect the structure of Morse-Smale semigroups with only equilibrium points, introducing generalized hyperbolicity and transversality concepts.

## Contribution

It introduces new notions of hyperbolicity and transversality applicable to non-differentiable perturbations of Morse-Smale semigroups, expanding the theoretical framework.

## Key findings

- Structural stability of equilibrium points under Lipschitz perturbations
- Generalized hyperbolicity and transversality concepts
- Behavior of connections between equilibria under perturbations

## Abstract

In this paper we will deal with Lipschitz continuous perturbations of Morse-Smale semigroups with only equilibrium points as critical elements. We study the behavior of the structure of equilibrium points and their connections when subjected to non-differentiable perturbations. To this end we define more general notions of \emph{hyperbolicity} and \emph{transversality}, which do not require differentiability.