Topological pressure for discontinuous semiflows and a variational principle for impulsive dynamical systems

Abstract

We introduce four, a priori different, concepts of topological pressure for possibly discontinuous semiflows acting on a compact metric space and observe that they all agree with the classical one when restricted to the continuous setting. Moreover, for a class of impulsive semiflows, which appear to be examples of discontinuous systems, we prove a variational principle. As a consequence, we conclude that for this class of systems the four notions of pressure coincide and, moreover, they also coincide with a concept of the topological pressure introduced in [3].