复杂性 影印版 物理学中的递阶结构和标度2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

复杂性 影印版 物理学中的递阶结构和标度PDF格式电子书版下载

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Part 1 Phenomenology and models1

Chapter 1 Introduction3

1.1 Statement of the problem3

1.2 Historical perspective7

1.3 Self-generated complexity9

Chapter 2 Examples of complex behaviour12

2.1 Instabilities in fluids13

2.1.1 Temporally"complex"dynamics13

2.1.2 Spatio-temporal"complexity"15

2.2 Turbulence17

2.3 Biological and chemical reactions19

2.4 Optical instabilities21

2.5 Growth phenomena23

2.6 DNA26

2.6.1 The genetic code27

2.6.2 Structure and function29

Chapter 3 Mathematical models32

3.1 Reduction methods for partial differential equations33

3.2 Ordinary differential equations37

3.3 Mappings39

3.3.1 Strange attractors41

3.4 Cellular automata48

3.4.1 Regular rules51

3.4.2 Chaotic rules53

3.4.3 "Complex"rules53

3.5 Statistical mechanical systems57

3.5.1 Spin glasses60

3.5.2 Optimization and artificial neural networks64

Part 2 Mathematical tools67

Chapter 4 Symbolic representations of physical systems69

4.1 Encoding in nonlinear dynamics70

4.2 Shifts and invariant sets76

4.2.1 Shift dynamical systems77

4.3 Languages78

4.3.1 Topological entropy81

4.3.2 Substitutions82

Chapter 5 Probability,ergodic theory,and information85

5.1 Measure-preserving transformations86

5.2 Stochastic processes89

5.3 Time-evolution operators93

5.4 Correlation functions96

5.5 Ergodic theory100

5.5.1 Spectral theory and isomorphism104

5.5.2 Shift dynamical systems105

5.5.3 What is the"generic"behaviour？107

5.5.4 Approximation theories108

5.6 Information,entropy,and dimension109

Chapter 6 Thermodynamic formalism119

6.1 Interactions119

6.2 Statistical ensembles123

6.2.1 Generalized entropies123

6.2.2 Generalized dimensions128

6.3 Phase transitions132

6.3.1 Critical exponents,universality,and renormalization134

6.3.2 Disordered systems141

6.4 Applications148

6.4.1 Power spectral measures and decay of correlation functions148

6.4.2 Thermodynamics of shift dynamical systems151

Part 3 Formal characterization of complexity163

Chapter 7 Physical and computational analysis of symbolic signals165

7.1 Formal languages,grammars,and automata166

7.1.1 Regular languages167

7.1.2 Context-free languages170

7.1.3 Context-sensitive languages175

7.1.4 Unrestricted languages177

7.1.5 Other languages183

7.2 Physical characterization of formal languages184

7.2.1 Regular languages184

7.2.2 Context-free languages187

7.2.3 DOL languages190

7.2.4 Context-sensitive and recursively enumerable languages197

7.3 Computational characterization of physical systems and mathematical models198

7.3.1 Dynamics at the borderline with chaos198

7.3.2 Quasicrystals200

7.3.3 Chaotic maps202

7.3.4 Cellular automata203

7.3.5 Relationship between Turing machines and dynamical systems207

7.3.6 Nucleotide sequences209

7.3.7 Discussion211

Chapter 8 Algorithmic and grammatical complexities213

8.1 Coding and data compression214

8.2 Model inference219

8.3 Algorithmic information226

8.3.1 P-NP problems230

8.4 Lempel-Ziv complexity233

8.5 Logical depth235

8.6 Sophistication237

8.7 Regular-language and set complexities240

8.8 Grammatical complexity243

Chapter 9 Hierarchical scaling complexities248

9.1 Diversity of trees249

9.1.1 Horton-Strahler indices252

9.2 Effective-measure and forecasting complexity253

9.3 Topological exponents255

9.4 Convergence of model predictions260

9.4.1 Global prediction260

9.4.2 Detailed prediction262

9.5 Scaling function270

Chapter 10 Summary and perspectives277

Appendix 1 The Lorenz model281

Appendix 2 The horseshoe map283

Appendix 3 Mathematical definitions285

Appendix 4 Lyapunov exponents,entropy,and dimension287

Appendix 5 Forbidden words in regular languages290

References293

Index311