Abstract
In the present chapter we consider two mathematical formalizations of the intuitive concept that iterating the dynamics \(\varphi\) provides a “thorough mixing” of the space \((X,\varSigma,\mu )\). Whereas the main theme of the previous chapter, the mean ergodicity of the associated Koopman operator, involved the norm topology, now the weak topology of the associated Lp-spaces becomes important.
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Notes
- 1.
It may be mistaken to mix different wines, but old and new wisdom mix very well.
- 2.
Der Kaukasische Kreidekreis, Szene 1; Edition Suhrkamp ⋅ Translation from: The Caucasian Chalk Circle, translated by Stefan S. Brecht, James Stern, Heinemann 1996.
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© 2015 Tanja Eisner, Bálint Farkas, Markus Haase, and Rainer Nagel
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Eisner, T., Farkas, B., Haase, M., Nagel, R. (2015). Mixing Dynamical Systems. In: Operator Theoretic Aspects of Ergodic Theory. Graduate Texts in Mathematics, vol 272. Springer, Cham. https://doi.org/10.1007/978-3-319-16898-2_9
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