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arXiv · 1906.07495

Decompositions of dynamical systems induced by the Koopman operator

Kari Küster
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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.

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Kari Küster. 2019-07-09. Decompositions of dynamical systems induced by the Koopman operator. https://arxiv.org/abs/1906.07495

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