Lyapunov quasi-stable trajectories

Changming Ding. "Lyapunov quasi-stable trajectories." Fundamenta Mathematicae 220.2 (2013): 139-154. <http://eudml.org/doc/282936>.

@article{ChangmingDing2013,
abstract = {We introduce the notions of Lyapunov quasi-stability and Zhukovskiĭ quasi-stability of a trajectory in an impulsive semidynamical system defined in a metric space, which are counterparts of corresponding stabilities in the theory of dynamical systems. We initiate the study of fundamental properties of those quasi-stable trajectories, in particular, the structures of their positive limit sets. In fact, we prove that if a trajectory is asymptotically Lyapunov quasi-stable, then its limit set consists of rest points, and if a trajectory in a locally compact space is uniformly asymptotically Zhukovskiĭ quasi-stable, then its limit set is a rest point or a periodic orbit. Also, we present examples to show the differences between variant quasi-stabilities. Further, some sufficient conditions are given to guarantee the quasi-stabilities of a prescribed trajectory.},
author = {Changming Ding},
journal = {Fundamenta Mathematicae},
keywords = {impulsive semidynamical system; Lyapunov quasi-stable; limit set; periodic orbit},
language = {eng},
number = {2},
pages = {139-154},
title = {Lyapunov quasi-stable trajectories},
url = {http://eudml.org/doc/282936},
volume = {220},
year = {2013},
}

TY - JOUR
AU - Changming Ding
TI - Lyapunov quasi-stable trajectories
JO - Fundamenta Mathematicae
PY - 2013
VL - 220
IS - 2
SP - 139
EP - 154
AB - We introduce the notions of Lyapunov quasi-stability and Zhukovskiĭ quasi-stability of a trajectory in an impulsive semidynamical system defined in a metric space, which are counterparts of corresponding stabilities in the theory of dynamical systems. We initiate the study of fundamental properties of those quasi-stable trajectories, in particular, the structures of their positive limit sets. In fact, we prove that if a trajectory is asymptotically Lyapunov quasi-stable, then its limit set consists of rest points, and if a trajectory in a locally compact space is uniformly asymptotically Zhukovskiĭ quasi-stable, then its limit set is a rest point or a periodic orbit. Also, we present examples to show the differences between variant quasi-stabilities. Further, some sufficient conditions are given to guarantee the quasi-stabilities of a prescribed trajectory.
LA - eng
KW - impulsive semidynamical system; Lyapunov quasi-stable; limit set; periodic orbit
UR - http://eudml.org/doc/282936
ER -