Lyapunov quasi-stable trajectories

• Autorzy: Changming Ding
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H20: Topological dynamics
• 37B25: Lyapunov functions and stability; attractors, repellers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 220
• Numer: 2
• Strony: 139-154

Daty

wydano

2013

Twórcy

autor

Changming Ding

• School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P.R. China

Identyfikatory

DOI

10.4064/fm220-2-4