What can Koopmanism do for attractors in dynamical systems?
Dynamical Systems
2019-03-12 v4 Functional Analysis
Abstract
We characterize the longterm behavior of a semiflow on a compact space 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.
Keywords
Cite
@article{arxiv.1902.07487,
title = {What can Koopmanism do for attractors in dynamical systems?},
author = {Viktoria Kühner},
journal= {arXiv preprint arXiv:1902.07487},
year = {2019}
}