An impulsive semiflow is prescribed by three ingredients: a continuous semiflow on a compact metric space X which governs the state of the system between impulses; a set D ⊂ X where the flow undergoes some abrupt perturbations, whose duration is, however, negligible in comparison with the time length of the whole process; and an impulsive function I: D → X which specifies how a jump event happens each time a trajectory of the flow hits D, whose action may be a source of discontinuities on the trajectories. We will establish sufficient conditions for the invariance of the non-wandering sets, except the discontinuity points, and for the existence of probability measures which are invariant by such dynamical systems.

This is a joint work with J. F. Alves.