TY - JOUR
AU - Ding, Changming
PY - 2016/04/12
Y2 - 2023/04/01
TI - Limit sets in impulsive semidynamical systems
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 43
IS - 1
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2014.007
SP - 97 - 115
AB - In this paper, we establish severalfundamental properties in impulsive semidynamical systems. First, weformulate a counterpart of the continuous dependence on the initialconditions for impulsive dynamical systems, and also establish someequivalent properties. Second, we present several theorems similarto the PoincarĂ©-Bendixson theorem for two-dimensional impulsivesystems, i.e if the omega limit set of a bounded infinitetrajectory (with an infinite number of impulses) contains no restpoints, then there exists an almost recurrent orbit in the limitset. Further, if the omega limit set contains an interior point,then it is a chaotic set; otherwise, if the limit set contains nointerior points, then the limit set contains a periodic orbit or a Cantor-type minimal set in which each orbit is almost recurrent.
ER -