Abstract
We give a short introduction to ergodic theory and its applications to topological dynamical systems. First we study the general properties of measure preserving transformations. Then we introduce the concepts of ergodicity, mixing, and exactness that describe different levels of chaotic behavior of the deterministic dynamics. The classic Birkhoff pointwise ergodic theorem and von Neumann mean ergodic theorem are stated, and some characteristics of ergodicity, mixing and exactness in terms of function sequences convergence are also presented.
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© 2009 Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg
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Ding, J., Zhou, A. (2009). Rudiments of Ergodic Theory. In: Statistical Properties of Deterministic Systems. Tsinghua University Texts. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85367-1_3
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DOI: https://doi.org/10.1007/978-3-540-85367-1_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85366-4
Online ISBN: 978-3-540-85367-1
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