Abstract
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.
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© 2009 Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg
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Ding, J., Zhou, A. (2009). Frobenius-Perron Operators. In: Statistical Properties of Deterministic Systems. Tsinghua University Texts. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85367-1_4
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DOI: https://doi.org/10.1007/978-3-540-85367-1_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85366-4
Online ISBN: 978-3-540-85367-1
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