Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical Systems
Dynamical Systems
2020-03-11 v1
Abstract
In this paper, we develop the Koopman operator theory for dynamical systems with symmetry. In particular, we investigate how the Koopman operator and eigenfunctions behave under the action of the symmetry group of the underlying dynamical system. Further, exploring the underlying symmetry, we propose an algorithm to construct a global Koopman operator from local Koopman operators. In particular, we show, by exploiting the symmetry, data from all the invariant sets are not required for constructing the global Koopman operator; that is, local knowledge of the system is enough to infer the global dynamics.
Keywords
Cite
@article{arxiv.2003.04870,
title = {Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical Systems},
author = {Subhrajit Sinha and Sai P. Nandanoori and Enoch Yeung},
journal= {arXiv preprint arXiv:2003.04870},
year = {2020}
}