Equilibrium states for impulsive semiflows

TL;DR

This paper studies impulsive semiflows on compact metric spaces, establishing conditions for equilibrium states, generalizing topological pressure, and proving a variational principle for discontinuous systems.

Contribution

It introduces a framework for equilibrium states in impulsive semiflows, extending classical thermodynamic formalism to discontinuous dynamical systems.

Findings

Established sufficient conditions for existence and uniqueness of equilibrium states.

Generalized topological pressure to impulsive semiflows.

Proved a variational principle linking pressure and measure-theoretic entropy.

Abstract

We consider impulsive semiflows defined on compact metric spaces and give sufficient conditions, both on the semiflows and the potentials, for the existence and uniqueness of equilibrium states. We also generalize the classical notion of topological pressure to our setting of discontinuous semiflows and prove a variational principle.