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What can Koopmanism do for attractors in dynamical systems?

Research paper by Viktoria Kühner

Indexed on: 20 Feb '19Published on: 20 Feb '19Published in: arXiv - Mathematics - Dynamical Systems



Abstract

We characterize the longterm behavior of a semiflow on a compact space $K$ by asymptotic properties of the corresponding Koopman semigroup. In particular, we compare different concepts of attractors, such as asymptotically stable attractors, Milnor attractors and centers of attraction. Furthermore, we give a characterization for the minimal attractor for each mentioned property. The main aspect is that we only need techniques and results for linear operator semigroups, since the Koopman semigroup permits a global linearization for a possibly non-linear semiflow.