A Variational principle for a class of discontinuous dynamical systems

Carlos Vásquez (PUC Valparaíso)

The variational principle claims that for continuous dynamical systems defined on compact metric spaces, the topological entropy is the supremum of the metric entropies associated to the invariant measures of the system. If the transformation (or flow) is not continuous, then the existence of invariant measures is not guaranteed. The goal of this talk is to discuss the existence of a variational principle for a class of measurable discontinuous semi-flows called impulsive systems. This discussion is based on a work in progress join with J. F. Alves and M. Carvalho (Univ. of Porto).