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Random Delta-Hausdorff-attractors

The second author is supported by the DFG-SPP 1590

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  • Global random attractors and random point attractors for random dynamical systems have been studied for several decades. Here we introduce two intermediate concepts: Δ-Hausdorff-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-Hausdorff-attractors for different values of Δ. It seems that both concepts are new even in the context of deterministic dynamical systems.

    Mathematics Subject Classification: Primary: 37H99, 37B25, 37C70; Secondary: 37H10.


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