符号动力学是粗粒化描述的动力学，能够给出对系统中周期性无序运动的严格分类。近年来，它被用到了以常微分方程，一维、二维映射所描述的非线性系统之中。《实用符号动力学与混沌 (第二版）(英文版)》将帮助非线性科学和工程领域的研究人员掌握这一有力工具。

PrefacefortheSecondEdition
Preface
1Introduction
1.1DynamicalSystems
1.1.1PhaseSpaceandOrbits
1.1.2ParametersandBifurcationofDynamicalBehavior
1.1.3ExamplesofDynamicalSystems
1.2SymbolicDynamicsasCoarse-GrainedDescriptionofDynamics--
1.2.1Fine-GrainedandCoarse-GrainedDescriptions
1.2.2SymbolicDynamicsastheSimplestDynamics
1.3AbstractversusAppliedSymbolicDynamics
1.3.1AbstractSymbolicDynamics
1.3.2AppliedSymbolicDynamics
1.4LiteratureonSymbolicDynamics
2SymbolicDynamicsofUnimodalMapsPrefacefortheSecondEdition
Preface
1Introduction
1.1DynamicalSystems
1.1.1PhaseSpaceandOrbits
1.1.2ParametersandBifurcationofDynamicalBehavior
1.1.3ExamplesofDynamicalSystems
1.2SymbolicDynamicsasCoarse-GrainedDescriptionofDynamics--
1.2.1Fine-GrainedandCoarse-GrainedDescriptions
1.2.2SymbolicDynamicsastheSimplestDynamics
1.3AbstractversusAppliedSymbolicDynamics
1.3.1AbstractSymbolicDynamics
1.3.2AppliedSymbolicDynamics
1.4LiteratureonSymbolicDynamics
2SymbolicDynamicsofUnimodalMaps
2.1SymbolicSequencesinUnimodalMaps
2.1.1NumericalOrbitandSymbolicSequence
2.1.2SymbolicSequenceandFunctionalComposition
2.1.3TheWord-LiftingTechnique
2.2TheQuadraticMap
2.2.1AnOver-SimplifiedPopulationModel
2.2.2BifurcationDiagramoftheQuadraticMap
2.2.3DarkLinesintheBifurcationDiagram
2.3OrderingofSymbolicSequencesandtheAdmissibilityCondition
2.3.1PropertyofMonotoneFhnctions
2.3.2TheOrderingRule
2.3.3DynamicalInvariantRangeandKneadingSequence
2.3.4TheAdmissibilityCondition
2.4ThePeriodicWindowTheorem
2.4.1ThePeriodicWindowTheorem
2.4.2ConstructionofMedianWords
2.4.3TheMSSTableofKneadingSequences
2.4.4NomenclatureofUnstablePeriodicOrbits
2.5CompositionRules
2.5.1The*-Composition
2.5.2GeneralizedCompositionRule
2.5.3ProofoftheGeneralizedCompositionRule
2.5.4ApplicationsoftheGeneralizedCompositionRule
2.5.5FurtherRemarksonCompositionRules
2.6Coarse-GrainedChaos
2.6.1ChaosintheSurjectiveUnimodalMap
2.6.2Chaosinpλ∞Maps
2.7TopologicalEntropy
2.8PiecewiseLinearMapsandMetricRepresentationofSymbolicSequences
2.8.1TheTentMapandShiftMap
..
3MapswithMultipleCriticalPoints
4SymbolicDynamicsofCircleMaps
5SymbolicDynamicsofTwo-DimensionalMaps
6ApplicationtoOrdinaryDifferentialEquations
7CountingtheNumberofPeriodicOrbits
8SymbolicDynamicsandGrammaticalComplexity
9SymbolicDynamicsandKnotTheory
10Appendix
References
Index

郝柏林，中国科学院理论物理研究所研究员，复旦大学教授，中国科学院院士，曾任中国科学院理论物理所所长。郑伟谋，中国科学院理论物理研究所研究员，博士生导师。获国家自然科学二等奖等多项奖励。