Attractor-repeller pair, Morse decomposition and Lyapunov function for random dynamical systems

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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.
17 pages, Latex

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Dynamical Systems, 37H99, 37B25, 37B55

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http://salesiana.dossiersoluciones.com/handle/123456789/113825

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606205
 http://arxiv.org/abs/math/0606205

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arXiv