Random Delta-Hausdorff-attractors

2017/03/31 by Scheutzow, Michael, Wilke-Berenguer, Maite
#37B25 #37C70 #37H10 #37H99 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1703.10962

Abstract

Global random attractors and random point attractors for random dynamical systems have been studied for several decades. Here we introduce two intermediate concepts: Δ-attractors are characterized by attracting all deterministic compact sets of Hausdorff dimension at most Δ, where Δ is a non-negative number, while cc-attractors attract all countable compact sets. We provide two examples showing that a given random dynamical system may have various different Δ-attractors for different values of Δ. It seems that both concepts are new even in the context of deterministic dynamical systems.

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