On Semicontinuity in Impulsive Dynamical Systems

• Autorzy: Krzysztof Ciesielski
• Języki publikacji: EN

Abstrakty

EN

In the important paper on impulsive systems [K1] several notions are introduced and several properties of these systems are shown. In particular, the function ϕ which describes "the time of reaching impulse points" is considered; this function has many important applications. In [K1] the continuity of this function is investigated. However, contrary to the theorem stated there, the function ϕ need not be continuous under the assumptions given in the theorem. Suitable examples are shown in this paper. We characterize the function ϕ from the point of view of its semicontinuity. Also, we show the analogous properties for impulsive systems given by semidynamical systems. In the last section we investigate the continuity properties of the escape time function in impulsive systems.

Kategorie tematyczne

• 54H20: Topological dynamics
• 34A37: Differential equations with impulses
• 37B99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 1
• Strony: 71-80

Daty

wydano

2004

Twórcy

autor

Krzysztof Ciesielski

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

Identyfikatory

DOI

10.4064/ba52-1-8