Titlebook: Statistical Properties of Deterministic Systems; Jiu Ding,Aihui Zhou Book 20091st edition Springer-Verlag Berlin Heidelberg 2009 Approxima

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,Invariant Measures—Existence,rs 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

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,Invariant Measures—Computation,ant method and its direct extension to multi-dimensional transformations. Then we study the piecewise linear Markov method proposed by the authors for one-and multidimensional transformations. We present Li’s pioneering work solving Ulam’s conjecture for the Lasota-Yorke class of interval mappings,

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Applications of Invariant Measures,tion of the speed of decay of correlations. Then we present Li-Yorke’s work on the application of stationary densities of small variation to random number generation. Two modern applications in the last decade are sketched in the final two sections. One is about the transfer operator in molecular co

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