Flows of characteristic 0+ in impulsive semidynamical systems

In this paper, as in [E.M. Bonotto, M. Federson, Topological conjugation and asymptotic stability in impulsive semidynamical systems, J. Math. Anal. Appl. (2006), doi:10.1016/j.jmaa.2006.03.042], we continue to study the dynamics of flows defined in impulsive semidynamical systems (X,π;M,I), where X is a metric space, (X,π) is a semidynamical system, M denotes an impulsive set and I is an impulsive operator. We generalize some results of non-impulsive flows of characteristic 0+ () for systems with impulses. In particular, we state conditions so that the limit set of an impulsive system of is either a periodic orbit or a single rest point. We also give conditions for a subset H in (X,π;M,I) to be globally asymptotically stable in the impulsive system, provided the flow is of .