准混沌冲击振子 : 重正化，符号动力学及运动迁移现象

1 Introduction1.1 Kicked oscillators1.2 Poincare sections1.3 Crystalline symmetry1.4 Stochastic webs1.5 Normal and anomalous diffusive behavior1.6 The sawtooth web map1.7 Renormalizability1.8 Long-time asymptotics1.9 Linking local and global behavior1.10 Organization of the bookReferences2 Renormalizability of the Local Map2.1 Heuristic approach to renormalizability2.1.1 Generalized rotations2.1.2 Natural return map tree2.1.3 Examples2.2 Quadratic piecewise isometries2.2.1 Arithmetic preliminaries2.2.2 Domains2.2.3 Geometric transformations on domains2.2.4 Scaling sequences2.2.5 Periodic orbits2.2.6 Recursive tiling2.2.7 Computer-assisted proofs2.3 Three quadratic models2.3.1 Modell2.3.2 Modelll2.3.3 Model III2.4 Proofofrenormalizability2.5 Structure of the discontinuity set2.5.1 Modell2.5.2 Modellll2.6 More general renormalization2.7 The π/7 modelReferences3 Symbolic Dynanucs3.1 Symbolic representation of the residual set3.1.1 Hierarchical symbol strings3.1.2 Eventually periodic codes3.1.3 Simplified codes for quadratic models3.2 Dynamical updating of codes3.3 Admissibility3.3.1 Quadratic example3.3.2 Models I, II, and III3.3.3 Cubic example3.4 MinimalityReferences4 Dimensions and Measures4.1 Hausdorff dimension and Hausdorff measure4.2 Construction of the measure4.3 Simplification for quadratic irrational4.4 A complicated example； Model II4.5 Discontinuity set in Model III4.6 Multifractal residual set of the π/7 model4.7 Asymptotic factorization4.8 Telescoping4.9 Unique ergodicity for each ∑（i）4.10 Multifractal spectrum of recurrence time dimensions4.10.1 Auxiliary measures and dimensions4.10.2 Simpler calculation of the recurrence time dimensions4.10.3 Recurrence time spectrum for the π/7 modelReferences5 Global Dynanucs5.1 Global expansivity5.1.1 Lifting the return map PK （O）5.1.2 Lifting the higher-level return maps5.2 Long-time asymptotics5.3 Quadratic examples5.4 Cubic examples5.4.1 Orbits in the （O,k,6∞） sectors……6 Transport7 Hamiltonian Round-OffAppendix A Data TablesAppendix B The CodometerIndexColor Figure Index

　　《准混沌冲击振子：重正化符号动力学及运动迁移现象（英文版）》介绍了准混沌运动研究的最新进展，讨论了动力系统中有序运动与无序运动交界处的复杂的动力学分支行为。准混沌运动是由具有自相似结构的稳定运动岛邻域附近运动轨迹的吸引性来刻画的，并且其相空间的位移是随时间的幂指数而渐近增加的。本专著全面、系统、自成体系地研究了一维经典冲击振子模型，并以完美的形式展示了准混沌运动在物理学和数学上的规则性和复杂性。　　《准混沌冲击振子：重正化符号动力学及运动迁移现象（英文版）》包含了目前文献中很多不曾涉及的新内容和新结果，它将激发物理学、应用数学的研究生和学者以及非线性动力学的专家对准混沌运动研究的极大兴趣，是一本难得的教科书或参考书。　　John H.Lowenstein为纽约大学物理系教授，非线性动力系统领域知名科学家，长期专注于一维冲击振子的动力学行为研究并取得了丰硕的成果，其中包括：在低维混沌和准混沌哈密顿系统中的运动迁移现象，区间及多边形分段等距自相似结构的数学理论。