# Star flows: a characterization via Lyapunov functions

## TL;DR

This paper characterizes star flows using Lyapunov functions, providing conditions for strong homogeneity of singular sets and applying these results to singular hyperbolic sets in dynamical systems.

## Contribution

It introduces a Lyapunov function-based characterization of star flows and establishes conditions for strong homogeneity of singular sets, advancing the understanding of hyperbolic dynamics.

## Key findings

- Characterization of star property via Lyapunov functions
- Conditions for strong homogeneity of singular sets
- Results on singular hyperbolic sets for flows

## Abstract

In this work, it is presented a characterization of star property for a $C^1$ vector field based on Lyapunov functions. It is also obtained conditions to strong homogeneity for singular sets by using the notion of infinitesimal Lyapunov functions. As an application, we obtain some results related to singular hyperbolic sets for flows.