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Topological conjugation and asymptotic stability in impulsive semidynamical systems. (English) Zbl 1162.37008

Summary: We prove several results concerning topological conjugation of two impulsive semidynamical systems. In particular, we prove that the homeomorphism which defines the topological conjugation takes impulsive points to impulsive points; it also preserves limit sets, prolongational limit sets and properties as the minimality of positive impulsive orbits as well as stability and invariance with respect to the impulsive system. We also present the concepts of attraction and asymptotic stability in this setting and prove some related results.

MSC:

37B25 Stability of topological dynamical systems
34A37 Ordinary differential equations with impulses
54H20 Topological dynamics (MSC2010)
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