A variational principle for impulsive semiflows

TL;DR

This paper extends the concept of topological entropy to impulsive semiflows on compact metric spaces by establishing a variational principle, thereby advancing the understanding of discontinuous dynamical systems.

Contribution

It introduces a variational principle for impulsive semiflows, generalizing classical entropy notions to systems with discontinuities.

Findings

Established a variational principle for impulsive semiflows.

Generalized topological entropy to discontinuous semiflows.

Provided a framework for analyzing impulsive dynamical systems.

Abstract

We consider impulsive semiflows defined on compact metric spaces and deduce a variational principle. In particular, we generalize the classical notion of topological entropy to our setting of discontinuous semiflows.