✦ LIBER ✦

The limit sets of uniformly asymptotically Zhukovskij stable orbits

✍ Scribed by Changming Ding

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 278 KB
Volume: 47
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(04)90070-3

No coin nor oath required. For personal study only.

✦ Synopsis

In this article, we prove that the omega limit set of a uniformly asymptotically Zhukovskij stable orbit of a differential system in R n is a closed orbit or a fixed point and also it is a uniform attractor. Further, if the system is defined on a compact subset of R n and each orbit is uniformly asymptotically Zhukovskij stable, then the set of fixed points and closed orbits is finite.

📜 SIMILAR VOLUMES

Uniformly asymptotically Zhukovskij stab

Uniformly asymptotically Zhukovskij stable orbits

✍ Changming Ding; J.M. Soriano 📂 Article 📅 2005 🏛 Elsevier Science 🌐 English ⚖ 250 KB

This article deals with Zhukovskij stability of planar systems. We prove that if the omega limit set of a nonclosed orbit is a stable limit cycle, then, the orbit is uniformly asymptotically Zhukovskij stable. @ 2005 Elsevier Ltd. All rights reserved.

Periodicity of Limit Sets of Uniformly A

Periodicity of Limit Sets of Uniformly Asymptotically Poincaré Stable Orbits

✍ Xiao-Song Yang 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 54 KB

This paper shows the omega set of a uniformly asymptotically Poincare stable órbit of an autonomous dynamical system is a periodic orbit.

On the behavior of orbits of uniformly s

On the behavior of orbits of uniformly stable semigroups at infinity

✍ V. I. Horbachuk; M. L. Horbachuk 📂 Article 📅 2006 🏛 Springer 🌐 English ⚖ 283 KB

Asymptotic expansion in the case of a st

Asymptotic expansion in the case of a stable limit law. I

✍ G. Christoph 📂 Article 📅 1982 🏛 Springer 🌐 English ⚖ 629 KB

Phase Asymptotic Semiflows, Poincaré's C

Phase Asymptotic Semiflows, Poincaré's Condition, and the Existence of Stable Limit Cycles

✍ Michael Y. Li; James S. Muldowney 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 793 KB

A concept of phase asymptotic semiflow is defined. It is shown that any Lagrange stable orbit at which the semiflow is phase asymptotic limits to a stable periodic orbit. A Lagrange stable solution of a C 1 differential equation is considered. When the second compound of the variational equation wit

Asymptotic Limit of the Bayes Actions Se

Asymptotic Limit of the Bayes Actions Set Derived from a Class of Loss Functions

✍ Christophe Abraham 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 223 KB

Similarly to the determination of a prior in Bayesian Decision theory, an arbitrarily precise determination of the loss function is unrealistic. Thus, analogously to global robustness with respect to the prior, one can consider a set of loss functions to describe the imprecise preferences of the dec