On Semicontinuity in Impulsive Dynamical Systems

Krzysztof Ciesielski. "On Semicontinuity in Impulsive Dynamical Systems." Bulletin of the Polish Academy of Sciences. Mathematics 52.1 (2004): 71-80. <http://eudml.org/doc/280474>.

@article{KrzysztofCiesielski2004,
abstract = {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.},
author = {Krzysztof Ciesielski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {impulsive systems; semicontinuity; semidynamical systems},
language = {eng},
number = {1},
pages = {71-80},
title = {On Semicontinuity in Impulsive Dynamical Systems},
url = {http://eudml.org/doc/280474},
volume = {52},
year = {2004},
}

TY - JOUR
AU - Krzysztof Ciesielski
TI - On Semicontinuity in Impulsive Dynamical Systems
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 1
SP - 71
EP - 80
AB - 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.
LA - eng
KW - impulsive systems; semicontinuity; semidynamical systems
UR - http://eudml.org/doc/280474
ER -