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

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dc.creatorLiu, Zhenxin
dc.creatorJi, Shuguan
dc.creatorSu, Menglong
dc.date2006-06-09
dc.date.accessioned2026-07-07T07:17:07Z
dc.date.available2026-07-07T07:17:07Z
dc.descriptionIn 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.
dc.description17 pages, Latex
dc.identifierhttps://arxiv.org/abs/math/0606205
dc.identifierhttp://arxiv.org/abs/math/0606205
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113825
dc.subjectDynamical Systems
dc.subject37H99, 37B25, 37B55
dc.titleAttractor-repeller pair, Morse decomposition and Lyapunov function for random dynamical systems
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