On Stability in Impulsive Dynamical Systems

Tom 52 / 2004

Krzysztof Ciesielski Bulletin Polish Acad. Sci. Math. 52 (2004), 81-91 MSC: Primary 37B25; Secondary 54H20, 34A37. DOI: 10.4064/ba52-1-9


Several results on stability in impulsive dynamical systems are proved. The first main result gives equivalent conditions for stability of a compact set. In particular, a generalization of Ura's theorem to the case of impulsive systems is shown. The second main theorem says that under some additional assumptions every component of a stable set is stable. Also, several examples indicating possible complicated phenomena in impulsive systems are presented.


  • Krzysztof CiesielskiMathematics Institute
    Jagiellonian University
    Reymonta 4
    30-059 Kraków, Poland

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