Federal University of Rio de Janeiro
Abstract :: Impulsive dynamical systems (IDS) can be interpreted as suitable mathematical models of real world phenomena that display abrupt changes in their behaviour. More precisely, an IDS is described by three objects: a continuous semiflow on a space X; a set D contained in X where the flow experiments sudden perturbations; and an impulsive function from D to X, which determines the change in the trajectory each time it collides with the impulsive set D.
In spite of their great range of applications, IDS have started being studied from the viewpoint of ergodic theory only recently.
A key challenge, inherent to the dynamics, is that in general, an impulsive semiflow is not continuous.
In this talk I will give an overview of some recent results on the ergodic theory of Impulsive semiflows. I will discuss in more details sufficient conditions on the semiflow and the potential for the existence and uniqueness of the corresponding equilibrium states.