On equilibrium states for impulsive semiows.**
Jaqueline Siqueira (PUC-Rio)
**Impulsive dynamical systems may be interpreted as suitable mathematical models of real world phenomena. They display abrupt changes in their behaviour, and are described by three objects: a continuous semiow on a metric space X; a set D contained in X where the ow experiments sudden perturbations; and an impulsive function I : D -> X which determines the change on a trajectory each time it collides with the impulsive set D. We consider impulsive semiows which are dened on compact metric spaces and we give sucient conditions, both on the semiows and on the potentials, for the existence and the uniqueness of equilibrium states. We also generalize the classical notion of topological pressure to our setting of discontinuous semiows and prove a variational principle. This is a joint work with José Ferreira Alves and Maria de Fátima de Carvalho.