Attractor-repeller pair, Morse decomposition and Lyapunov function for random dynamical systems
Dynamical Systems
2007-05-23 v1
Abstract
In the stability theory of dynamical systems, Lyapunov functions play a fundamental role. In this paper, we study the attractor-repeller pair decomposition and Morse decomposition for compact metric space in the random setting. In contrast to [8], by introducing slightly stronger definitions of random attractor and repeller, we characterize attractor-repeller pair decompositions and Morse decompositions for random dynamical systems through the existence of Lyapunov functions. These characterizations, we think, deserve to be known widely.
Cite
@article{arxiv.math/0606205,
title = {Attractor-repeller pair, Morse decomposition and Lyapunov function for random dynamical systems},
author = {Zhenxin Liu and Shuguan Ji and Menglong Su},
journal= {arXiv preprint arXiv:math/0606205},
year = {2007}
}
Comments
17 pages, Latex