確定性系統(tǒng)的統(tǒng)計(jì)性質(zhì)

內(nèi)容概要

本書介紹的是確定性離散動力系統(tǒng)統(tǒng)計(jì)性質(zhì)的基本理論與計(jì)算方法，首先介紹了遍歷理論的一些經(jīng)典結(jié)果；然后著重研究了對應(yīng)于混沌映射的絕對連續(xù)不變測度的存在性與計(jì)算問題，這歸結(jié)于相應(yīng)的Frobenius—Perron算子的泛函分析與數(shù)值分析；最后本書介紹了Shannon熵、Kolmogorov熵、拓?fù)潇匾约癇oltzmann熵，并給出了不變測度的一些最新應(yīng)用．本書可作為數(shù)學(xué)、計(jì)算科學(xué)及工程專業(yè)的研究生教材或參考書。

書籍目錄

Chapter 1 Introduction　1.1 Discrete Deterministic Systems—from Order to Chaos　1.2 Statistical Study of Chaos　ExercisesChapter 2  Foundations of Measure Theory　2.1 Measures and Integration　2.2 Basic Integration Theory　2.3 Functions of Bounded Variation in One Variable　2.4 Functions of Bounded Variation in Several Variables　2.5 Compactness and Quasi—compactness　　2.5.1 Strong and Wleak Compactness　　2.5.2 Quasi-Compactness　ExercisesChapter 3 Rudiments of Ergodic Theory　3.1 Measure Preserving TransfcIrmations　3.2 Ergodicity,Mixing and Exactness　　3.2.1 Ergodicity　　3.2.2 Mixing and Exactness　3.3 Ergodic Theorems　3.4 Topological Dynamical Systems　ExercisesChapter 4 Frobenius-Perron Operators　4.1 Markov Operatorst　4.2 nobenius—Perron Operators　4.3 Koopman 0peratorst　4.4 Ergodicity and Frobenius—Perron Operators　4.5 Decomposition Theorem and Spectral Analysis　ExercisesChapter 5 Invariant Measures——Existence　5.1 General Existence Results　5.2 Piecewise Stretching Mappings　5.3 Piecewise Convex Mappings　5.4 Piecewise Expanding Transformations　Exercises.Chapter 6  Invariant Measures--Computation　61 Ulam’s Method for One—Dimensional Mappings　6.2 Ulam’S Method for N—dimensional Transformations　6.3 The Markov Method for One—Dimensional Mappings　6.4 The Markov Metho(~for N—dimensional Transformations　Exercises-Chapter 7 Convergence Rate Analysis　7.1 Error Estimates for Ulam’S Method.　7.2 More Explicit Error Estimates　7.3 Error Estimates for the Markov Method　ExercisesChapter 8 Entropy　8.1 Shannon Entropy　8.2 Kolmogorov Entropy　8.3 Topological Entropy　8.4 Boltzmann Entropy　8.5 Boltzmann Entropy and Frobenius—Perron Operators　ExercisesChapter 9  Applications of Invariant Measures　9.1 Decay of Correlations　9.2 Random Number Generationi　9.3 Conformational Dynamics of Bio—molecules4：　9.4 DS—CDMA in Wireless Communications　ExercisesBibliographyIndex

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