Stability of the global attractor under Markov-Wasserstein noise

Details Stability of the global attractor under Markov-Wasserstein noise Stability of the global attractor under Markov-Wasserstein noise

2011-03-17

arxiv.org/abs/1103.3401v1

Mathematics

Dynamical Systems

19 pages

Scientific paper

We develop a "weak Wa\.zewski 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.

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