In this chapter we discuss absence of non-trivial invariant sets in both the measure-theoretic and the topological setting, i.e., ergodicity and minimality. We also study spectral properties of Koopman operators, in particular, with connection to these properties. Weak and strong mixing are introduced and discussed very briefly as well.

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Minimality and Ergodicity

  • Tanja Eisner,
  • Bálint Farkas

摘要

In this chapter we discuss absence of non-trivial invariant sets in both the measure-theoretic and the topological setting, i.e., ergodicity and minimality. We also study spectral properties of Koopman operators, in particular, with connection to these properties. Weak and strong mixing are introduced and discussed very briefly as well.