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確定性系統(tǒng)的統(tǒng)計(jì)性質(zhì)

確定性系統(tǒng)的統(tǒng)計(jì)性質(zhì)

定 價(jià):¥48.00

作 者: 丁玖,周愛輝 編著
出版社: 清華大學(xué)出版社
叢編項(xiàng):
標(biāo) 簽: 微積分

ISBN: 9787302182962 出版時(shí)間: 2008-11-01 包裝: 精裝
開本: 16開 頁數(shù): 236 字?jǐn)?shù):  

內(nèi)容簡介

  《確定性系統(tǒng)的統(tǒng)計(jì)性質(zhì)》介紹的是確定性離散動(dòng)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(duì)應(yīng)于混沌映射的絕對(duì)連續(xù)不變測(cè)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《確定性系統(tǒng)的統(tǒng)計(jì)性質(zhì)》介紹了Shannon熵、Kolmogorov熵、拓?fù)潇匾约癇oltzmann熵,并給出了不變測(cè)度的一些最新應(yīng)用?!洞_定性系統(tǒng)的統(tǒng)計(jì)性質(zhì)》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。

作者簡介

  Jiu Ding,Aihui Zhou,Statistical Properties of Deterministic SystemsStatistical Properties of Deterministic Systems discusses the fundamental theory and computational methods of the statistical properties of deterministic discrete dynamical systems. After introducing some basic results from ergodic theory, two probIems related to the dynamical system are studied: first the existence of absolute continuous invariant measures, and then their computation. They correspond to the functional analysis and numerical analysis of the Frobenius-Perron operator associated with the dynamical system.The book can be used as a text for graduate students in applied mathematics and in computational mathematics; it can also serve as a reference book for researchers in the physical sciences, life sciences, and engineering.

圖書目錄

Chapter 1 Introduction
 1.1 Discrete Deterministic Systems—from Order to Chaos
 1.2 Statistical Study of Chaos
 Exercises
Chapter 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
 Exercises
Chapter 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
 Exercises
Chapter 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
 Exercises
Chapter 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
 Exercises
Chapter 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
 Exercises
Chapter 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
 Exercises
Bibliography
Index

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