Abstract
The existence problem of a stationary density to a Frobenius-Perron operator will be investigated. Three general existence theorems for Markov operators are presented with the help of the concepts of compactness, quasi-compactness, and constrictiveness. A powerful spectral decomposition theorem for constrictive Markov operators will be given. Then we prove the existence results for three concrete classes of transformations. They are the class of piecewise C2 and stretching interval mappings, the class of piecewise convex mappings with a weak repellor, and the class of multi-dimensional piecewise C2 and expanding 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). Invariant Measures—Existence. In: Statistical Properties of Deterministic Systems. Tsinghua University Texts. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85367-1_5
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DOI: https://doi.org/10.1007/978-3-540-85367-1_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85366-4
Online ISBN: 978-3-540-85367-1
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