Decompositions of dynamical systems induced by the Koopman operator
Dynamical Systems
2019-07-10 v3 Functional Analysis
Abstract
For a topological dynamical system we characterize the decomposition of the state space induced by the fixed space of the corresponding Koopman operator. For this purpose, we introduce a hierarchy of generalized orbits and obtain the finest decomposition of the state space into absolutely Lyapunov stable sets. Analogously to the measure-preserving case, this yields that the system is topologically ergodic if and only if the fixed space of its Koopman operator is one-dimensional.
Keywords
Cite
@article{arxiv.1906.07495,
title = {Decompositions of dynamical systems induced by the Koopman operator},
author = {Kari Küster},
journal= {arXiv preprint arXiv:1906.07495},
year = {2019}
}