Limit sets and the Poincaré–Bendixson Theorem in impulsive semidynamical systems

We consider semidynamical systems with impulse effects at variable times and we discuss some properties of the limit sets of orbits of these systems such as invariancy, compactness and connectedness. As a consequence we obtain a version of the Poincaré–Bendixson Theorem for impulsive semidynamical systems.