《準(zhǔn)混沌沖擊振子：重正化符號動力學(xué)及運動遷移現(xiàn)象（英文版）》介紹了準(zhǔn)混沌運動研究的最新進展，討論了動力系統(tǒng)中有序運動與無序運動交界處的復(fù)雜的動力學(xué)分支行為。準(zhǔn)混沌運動是由具有自相似結(jié)構(gòu)的穩(wěn)定運動島鄰域附近運動軌跡的吸引性來刻畫的，并且其相空間的位移是隨時間的冪指數(shù)而漸近增加的。本專著全面、系統(tǒng)、自成體系地研究了一維經(jīng)典沖擊振子模型，并以完美的形式展示了準(zhǔn)混沌運動在物理學(xué)和數(shù)學(xué)上的規(guī)則性和復(fù)雜性?！稖?zhǔn)混沌沖擊振子：重正化符號動力學(xué)及運動遷移現(xiàn)象（英文版）》包含了目前文獻中很多不曾涉及的新內(nèi)容和新結(jié)果，它將激發(fā)物理學(xué)、應(yīng)用數(shù)學(xué)的研究生和學(xué)者以及非線性動力學(xué)的專家對準(zhǔn)混沌運動研究的極大興趣，是一本難得的教科書或參考書。John H. Lowenstein為紐約大學(xué)物理系教授，非線性動力系統(tǒng)領(lǐng)域知名科學(xué)家，長期專注于一維沖擊振子的動力學(xué)行為研究并取得了豐碩的成果，其中包括：在低維混沌和準(zhǔn)混沌哈密頓系統(tǒng)中的運動遷移現(xiàn)象，區(qū)間及多邊形分段等距自相似結(jié)構(gòu)的數(shù)學(xué)理論。
1 Introduction 1.1 Kicked oscillators 1.2 Poincare sections 1.3 Crystalline symmetry 1.4 Stochastic webs 1.5 Normal and anomalous diffusive behavior 1.6 The sawtooth web map 1.7 Renormalizability 1.8 Long-time asymptotics 1.9 Linking local and global behavior 1.10 Organization of the book References 2 Renormalizability of the Local Map 2.1 Heuristic approach to renormalizability 2.1.1 Generalized rotations 2.1.2 Natural return map tree 2.1.3 Examples 2.2 Quadratic piecewise isometries 2.2.1 Arithmetic preliminaries 2.2.2 Domains 2.2.3 Geometric transformations on domains 2.2.4 Scaling sequences 2.2.5 Periodic orbits 2.2.6 Recursive tiling 2.2.7 Computer-assisted proofs 2.3 Three quadratic models 2.3.1 Modell 2.3.2 Modelll 2.3.3 Model III 2.4 Proofofrenormalizability 2.5 Structure of the discontinuity set 2.5.1 Modell 2.5.2 Modellll 2.6 More general renormalization 2.7 The π/7 model References 3 Symbolic Dynanucs 3.1 Symbolic representation of the residual set 3.1.1 Hierarchical symbol strings 3.1.2 Eventually periodic codes 3.1.3 Simplified codes for quadratic models 3.2 Dynamical updating of codes 3.3 Admissibility 3.3.1 Quadratic example 3.3.2 Models I, II, and III 3.3.3 Cubic example 3.4 Minimality References 4 Dimensions and Measures 4.1 Hausdorff dimension and Hausdorff measure 4.2 Construction of the measure 4.3 Simplification for quadratic irrational 4.4 A complicated example: Model II 4.5 Discontinuity set in Model III 4.6 Multifractal residual set of the π/7 model 4.7 Asymptotic factorization 4.8 Telescoping 4.9 Unique ergodicity for each ∑（i） 4.10 Multifractal spectrum of recurrence time dimensions 4.10.1 Auxiliary measures and dimensions 4.10.2 Simpler calculation of the recurrence time dimensions 4.10.3 Recurrence time spectrum for the π/7 model References 5 Global Dynanucs 5.1 Global expansivity 5.1.1 Lifting the return map PK （O） 5.1.2 Lifting the higher-level return maps 5.2 Long-time asymptotics 5.3 Quadratic examples 5.4 Cubic examples 5.4.1 Orbits in the （O,k,6∞） sectors …… 6 Transport 7 Hamiltonian Round-Off Appendix A Data Tables Appendix B The Codometer Index Color Figure Index
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