Flows of characteristic [formula omitted] in impulsive semidynamical systems

Abstract

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 + ( Ch 0 + ) for systems with impulses. In particular, we state conditions so that the limit set of an impulsive system of Ch 0 + 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 Ch 0 + .