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arXiv · 1703.10962

Random Delta-Hausdorff-attractors

Michael Scheutzow·Maite Wilke-Berenguer
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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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Michael Scheutzow, Maite Wilke-Berenguer. 2017-08-29. Random Delta-Hausdorff-attractors. https://arxiv.org/abs/1703.10962

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