Synchronisation of almost all trajectories of a random dynamical system

Julian Newman

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arXiv · 1511.08831

Synchronisation of almost all trajectories of a random dynamical system

Julian Newman

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Abstract

It has been shown by Le Jan that, given a memoryless-noise random dynamical system together with an ergodic distribution for the associated Markov transition probabilities, if the support of the ergodic distribution admits locally asymptotically stable trajectories, then there is a random attracting set consisting of finitely many points, whose basin of forward-time attraction includes a random full measure open set. In this paper, we present necessary and sufficient conditions for this attracting set to be a singleton; our result does not require the state space to be compact, but holds on general Lusin metric spaces.

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Julian Newman. 2016-01-09. Synchronisation of almost all trajectories of a random dynamical system. https://arxiv.org/abs/1511.08831

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