Decompositions of Dynamical Systems Induced by the Koopman Operator

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 s...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2021-03, Vol.47 (1), p.149-173
Main Author: Küster, K.
Format: Article
Language:English
Subjects:
Analysis
Decomposition
Dynamical systems
Mathematics
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Summary: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.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-021-0068-8