2009 | OriginalPaper | Buchkapitel
Frobenius-Perron Operators
verfasst von : Jiu Ding, Aihui Zhou
Erschienen in: Statistical Properties of Deterministic Systems
Verlag: Springer Berlin Heidelberg
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In this chapter we first introduce Markov operators and study their general properties. Then we define Frobenius-Perron operators, a special class of Markov operators that will be mainly studied in the book. We also present a decomposition theorem for the Frobenius-Perron operator and its spectral analysis. We employ the Frobenius-Perron operator and its dual operator, the Koopman operator, to study ergodicity, mixing, and exactness of chaotic transformations.