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Zhukovskij quasi-stable orbits of impulsive dynamical systems. (English) Zbl 1392.37029

Summary: This paper deals with the Zhukovskij quasi-stability of an orbit in a planar impulsive dynamical system. We prove that if the positive limit set of an orbit is an asymptotically stable limit cycle (an isolated periodic orbit), then the orbit is uniformly asymptotically Zhukovskij quasi-stable. Also, we prove that if an orbit is not eventually periodic and its positive limit set is a periodic orbit, then it is asymptotically Zhukovskij quasi-stable.

MSC:

37C75 Stability theory for smooth dynamical systems
37C27 Periodic orbits of vector fields and flows
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