@article{Ding_2016, title={Limit sets in impulsive semidynamical systems}, volume={43}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2014.007}, abstractNote={In this paper, we establish several
fundamental properties in impulsive semidynamical systems. First, we
formulate a counterpart of the continuous dependence on the initial
conditions for impulsive dynamical systems, and also establish some
equivalent properties. Second, we present several theorems similar
to the PoincarĂ©-Bendixson theorem for two-dimensional impulsive
systems, i.e if the omega limit set of a bounded infinite
trajectory (with an infinite number of impulses) contains no rest
points, then there exists an almost recurrent orbit in the limit
set. Further, if the omega limit set contains an interior point,
then it is a chaotic set; otherwise, if the limit set contains no
interior points, then the limit set contains a periodic orbit or a Cantor-type minimal set in which each orbit is almost recurrent.}, number={1}, journal={Topological Methods in Nonlinear Analysis}, author={Ding, Changming}, year={2016}, month={Apr.}, pages={97â€“115} }