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arXiv · 1902.07487

What can Koopmanism do for attractors in dynamical systems?

Viktoria Kühner
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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.

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Viktoria Kühner. 2019-02-20. What can Koopmanism do for attractors in dynamical systems?. https://arxiv.org/abs/1902.07487

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