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 ��/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 ��/7 model 4.7 Asymptotic factorization 4.8 Telescoping 4.9 Unique ergodicity for each �ƣ�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 ��/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�ޣ� sectors ���� 6 Transport 7 Hamiltonian Round-Off Appendix A Data Tables Appendix B The Codometer Index Color Figure Index