Stability of the global attractor under Markov-Wasserstein noise

Martin Kell

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Submission date: 17. Mar. 2011
Pages: 21
Bibtex
MSC-Numbers: 34D23, 37B35, 60B05, 60B10
Keywords and phrases: global attractor, random perturbation, Wasserstein space
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Abstract:
We develop a “weak Ważewski principle” for discrete and continuous time dynamical systems on metric spaces having a weaker topology to show that attractors can be continued in a weak sense. After showing that the Wasserstein space of a proper metric space is weakly proper we give a sufficient and necessary condition such that a continuous map (or semiflow) induces a continuous map (or semiflow) on the Wasserstein space. In particular, if these conditions hold then the global attractor, viewed as invariant measures, can be continued under Markov-type random perturbations which are sufficiently small w.r.t. the Wasserstein distance, e.g. any small bounded Markov-type noise and Gaussian noise with small variance will satisfy the assumption.