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　　《準混沌沖擊振子：重正化符號動力學及運動遷移現(xiàn)象（英文版）》介紹了準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雜的動力學分支行為。準混沌運動是由具有自相似結構的穩(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典沖擊振子模型，并以完美的形式展示了準混沌運動在物理學和數(shù)學上的規(guī)則性和復雜性。
　　《準混沌沖擊振子：重正化符號動力學及運動遷移現(xiàn)象（英文版）》包含了目前文獻中很多不曾涉及的新內容和新結果，它將激發(fā)物理學、應用數(shù)學的研究生和學者以及非線性動力學的專家對準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為紐約大學物理系教授，非線性動力系統(tǒng)領域知名科學家，長期專注于一維沖擊振子的動力學行為研究并取得了豐碩的成果，其中包括：在低維混沌和準混沌哈密頓系統(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構的數(shù)學理論。

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

　　Chapter 4
　　Here we focus on the measure-theoretic and fractal （ormultifractal） properties of the residual set of the local map. Theintroduction of Hausdorff dimension and Haus- dorff measure will beessential， later on， to formulating transport on interesting setsof Lebesgue measure zero. Using a transfer matrix to linksuccessive levels of the renormalization hierarchy， we calculate anontrivial spectrum of generalized dimensions for the π/7model.
　　Chapter 5
　　We now examine how the localreturn maps of a scaling sequence canbe lifted to the nfinite kicked-oscillator phase space. In somecases the resulting global translation vectors are globallyexpansive， increasing in length geometrically with increasinglevel. In such cases， we prove that the discontinuity-avoidingaperiodic orbits tend to infinity according to a power law. Westudy this phenomenon numerically in a number of examples. In theparticularly interesting case of the π/7 model， we see thatdifferent initial conditions can lead to a variety of asymptoticpower laws.
　　Chapter 6
　　A statistical formulation of the time evolution is presented inthis chapter， based on a coarse-grained probability distributionP（（m，n），t）. Once again， the renormaliz- ability of the models andespecially the recursive tiling property， serve as the organizingprinciples. We consider examples in which the probability issupported on the 2-dimensional periodic domains， but also onesrestricted to interesting lower- dimensional sets. Highly efficientcodometer updating allows us to investigate numerically asymptoticpower laws with log-periodic modulation.
　　Chapter 7
　　In this final chapter， we consider a different type of kickedoscillator dynamics， namely that of a Hamiltonian round-off map（Lowenstein et al， 1997; Lowenstein and Vivaldi， 1998， 2000）. Onceagain we have a local piecewise isometry which induces apermutation of 22. Although in this class of models all orbits areperiodic， one can still describe the long-time behaviorstatistically in terms of periodically and quasi-periodicallymodulated power laws. We study these both analytically and withhighly efficient numerical experiments.
　　Appendixes
　　For the sake of completeness， we include in the Appendix A anumber of data tables for the models which appear throughout thebook.ln addition， we have a short explanation of our implementationof the hierarchical symbolic dynamics， the codometer， in AppendixB.
　　……

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