Star Flows: A Characterization Via Lyapunov Functions

In this work, it is presented a characterization of star property for a \(C^1\) $C^1$ 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.