The limit sets of uniformly asymptotically Zhukovskij stable orbits

In this article, we prove that the omega limit set of a uniformly asymptotically Zhukovskij stable orbit of a differential system in Rn 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 Rn and each orbit is uniformly asymptotically Zhukovskij stable, then the set of fixed points and closed orbits is finite.