Авторизация
Поиск по указателям
Badii R., Politi A. — Complexity: Hierarchical structures and scaling in physics
Обсудите книгу на научном форуме Нашли опечатку?
Название: Complexity: Hierarchical structures and scaling in physicsАвторы: Badii R., Politi A. Аннотация: This is a comprehensive discussion of complexity as it arises in physical, chemical and biological systems, as well as in mathematical models of nature. The aim of this book is to illustrate the ways in which complexity manifests itself and to introduce a sequence of increasingly sharp mathematical methods for the classification of complex behavior. This book will be of interest to graduate students and researchers in physics (nonlinear dynamics, fluid dynamics, solid-state, cellular automata, stochastic processes, statistical mechanics and thermodynamics), mathematics (dynamical systems, ergodic and probability theory), information and computer science (coding, information theory and algorithmic complexity), electrical engineering and theoretical biology.
Язык: Рубрика: Физика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1997Количество страниц: 318Добавлена в каталог: 14.02.2014Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Ising — Lenz model 58 121 Isolated system 59 Jacobian determinant 41 Julia set 47 K-automorphism 103 Kam theorem 46 Kaplan — Yorke relation 154 289 Kesten theorem 202 Kneading sequence 244 Kolmogorov — Sinai, entropy 113 124 Kolmogorov — Sinai, theorem 113 Kolmogorov, complexity 226 Kolmogorov, length 17 34 Kolmogorov, scaling 36 Koopman operator 104 Kraft inequality 216 226 Kullback — Leibler distance 113 Laminar flow 15 Language 78—84 Language, extendible 79 Language, factorial 79 257 Language, power-free 83 Language, transitive 79 257 Laplace equation 26 Laser 21 Laser, instability 21 Laser, single-mode 34 Lattice-gas 120 Lattice-gas automata 57 Learning 219 Lebesgue integral 286 Lebesgue measure 285 Legendre transform 126 127 131 Lempel — Ziv complexity 233—235 Lexicographic order 49 79 Limit set 50 Linear bounded automaton 176 Liouville equation 95 Local dimension 128 287 Local entropy 287 Local scaling ratios 270 Local structure theory 92 Logical depth 235—237 Logistic map 44 95 132 134 275 Logistic map, complex 47 Lorenz model 34 274 282 Lozi map 73 Lyapunov exponents 42 44 45 101 208 257 288 Lyapunov exponents, local 276 Mandelbrot set 47 Manifold, stable 38 41 Manifold, unstable 38 41 MAP 39—48 71 86 Map, conservative 45 46 Map, dissipative 45 Map, one-dimensional 72 Mapping see "Map" Markov approximation 92 Markov average time 222 Markov chain 90 92 Markov chain, irreducible 91 Markov model 260 264 269 Markov operator 94 Markov partition 73 74 81 94 202 Markov process 93 120 185 222 Markov process, higher order 92 114 Markov shift 80 94 102 Maximal set 40 Maxwell — Bloch equations 34 Mean 96 mean field 63 Mean field, approximation 25 Mean field, cellular automata 92 Measure 285 Measure space 86 Measure, absolutely continuous 87 97 Measure, atomic see "Measure pure Measure, decomposition 87 Measure, Lebesgue 87 95 Measure, Liouville 96 Measure, natural 88 Measure, pure point 87 Measure, singular-continuous 88 Measure, SRB 88 Measure-preserving transformation 86—89 Memory 92 Messenger RNA 29 Metastable configuration 62 Metric complexity 264 273 276 Metric entropy 112 113 217 229 235 Metrically transitive system 101 Microstate 119 Minimal graph 169 Minimal program 227 Minimal system 77 82 84 224 229 Mixing 102 105 107 114 Mixing, strong 102 Mixing, weak 102 103 197 Mode-locking 46 Model convergence 260—270 Model inference 219—226 Monte Carlo method 58 Morse — Thue see "Substitution Morse Morse — Thue sequence 224 Multistability 15 Mutations 28 Mutual independence 90 Mutual information 114 246 Mutually singular measures 87 89 Myhill — Nerode theorem 169 n-cylinder 76 87 89 Navier — Stokes equations 13 35 Navier — Stokes equations, inviscid 35 Neural networks 64—66 Noise, 1/f 98 Nondeterministic graph 168 Nondeterministic Turing machine 231 Nonequilibrium 12 59 Nonhyperbolic attractor 43 Nonhyperbolic map 44 Nonhyperbolic phase 154 Nonstationary pattern 30 Nonstationary process 89 98 100 Nonwandering set 40 NP-complete language 232 nucleotides 26 One-dimensional map 94 Open systems 12 Optical instabilities 21—23 Optical turbulence 37 Optimal code 216 Optimization 64—66 Optimization problem 231 Order 20 Order-disorder transition 15 Ordinary differential equations 37—39 P-NP problems 230—233 Palindrome DNA sequence 30 210 Palindrome word 83 173 Partial differential equations 33—37 Partial dimension 117 288 Partition 70 86 Partition function, canonical 123 Partition function, effective 143 Partition function, isothermal-isobaric 129 Partition function, microcan onical 125 Partition, refinement 70 Patterns, nonstationary 30 Patterns, quasiperiodic 23 Patterns, spatial 14 15 17 19 21 Penrose tiling 201 Perfect space 76 Period-doubling 14 83 98 117 199 271 Period-doubling, cascade 44 Periodic orbit 41 77 Periodic point 47 73 Periodic signal 97 Phase space 37 Phase transition 58 60 132—148 151 190 258 269 274 276 Phase transition, continuous 133 Phase transition, first order 133 152 159 Phase transition, first order, anomalous 134 159 Phylum 27 Pisot — Vijayaraghavan (PV) number 196 199 Poincare map 39 Poincare recurrence theorem 101 Poincare section 39 73 Poincare surface 39 Power spectrum 96 148—151 188 190 Power spectrum, absolutely continuous 97 149 Power spectrum, pure-point 149 Power spectrum, recurrent 97 Power spectrum, singular-continuous 97 149 195 Power spectrum, transient 97 Power-spectral analysis 211 predictions 260—270 Prefix-preserving morphism 83 Primitive word 222 223 probability 87 Probability measure 86 Product map 106 Product topology 76 Promoter 30 Proteins 27 Pseudo-probability 265 267 Pseudolinear languages 189 Pumping lemma 169 171 224 Pushdown automaton 172 Quasicrystals 23 82 200—202 Quasilattice 200 Quasiperiodic signal 97 Quasiperiodicity 45 Quenched average 143 Radon — Nikodym theorem 87 Random energy model 143 Random fractals 141 Random multiplicative process 18 Random variable 89 Random walk 25 89 141 187 190 Random walk, self-avoiding 197 Randomness 98 226 246 Rational partition 246 Rayleigh — Benard convection 13 34 35 281 Reaction-diffusion 20 Reaction-limited aggregation 24 Recurrence 78 101 Recursive function, partial 183 Recursive function, total 183 Recursive language 181 Recursively enumerable language 180 Reduction methods 33—37 Redundancy 112 refinement 86 Regular expression 167 243 Regular languages 80 167—170 184—187 Relative entropy 113 264 Relatively dense set 78 Renewal system 81 Renormalization (of maps) 225 Renormalization group 134—141 Renormalization group, chaotic 140 147 266 Renormalized entropy 246 Renyi information 124 Replica method 143 Residual set 107 286 Reynolds number 17 Riddled basin 48 RLA 24 RNA 27 Roof map 74 80 94 225 Rotation number 45 46 Saddle 38 Scalar time series 118 Scaling 7 128 130 135 137 139 147 149 155 159 260 287 Scaling dynamics 262 266 269 273 Scaling function 270—276 Scaling function, fractal 276 Scaling hypothesis 135 Secondary structure in tRNA 210 Self-averaging functions 63 142 Self-delimiting program 227 Self-similarity 17 23 117 270 271 Sentential form 170 Shannon — McMillan — Breiman theorem 128 287 Sherrington — Kirkpatrick model 63 64 147 Shift dynamical system 76—78 105—107 Shift map 76 Signal reconstruction 223 simplicity 109 Simulated annealing 65 Sine model 62 Singular value decomposition 34 Singularity exponent 88 149 Skew product 44 149 Slaved variables 35 Smoluchowski equation 25 Sofic partition 81 Sofic system 80 81 Solenoid map 43 sophistication 237—240 Specific heat 128 Spectral theory (ergodic) 104 Spin glass 60—63 64 143 Stable manifold 38 41 Standard map 46 Stationary density 94 Stationary process 89 248 Statistical ensembles 123—132 Statistical independence 90 Statistical mechanics 57—66 Stochastic process 89—93 Strahler number 252 Strange Attractor 41—43 Strange nonchaotic attractor 149 199 Strange repeller 47 Stream function 281 Strict ergodicity 105 Strictly sofic system 80 81 169 185 203 256 String 78 Strong topology 107 Structural stability 41 43 Sturmian systems 105 201 229 Subharmonic 44 Subshift 77 Subshift of finite type 80 169 205 Substitution 82—84 222 Substitution, Dekking — Keane 197 Substitution, Fibonacci 83 192 Substitution, Morse — Thue 83 106 195 199 Substitution, Morse — Thue, ternary 83 Substitution, period-doubling 83 194 Substitution, Rudin — Shapiro 196 Support 97 Symbolic dynamical system see "Shift dynamical system" Symbolic dynamics 71 Symbolic sequence 70 Systems, conservative 32 37 Systems, dissipative 32 37 Systems, extended 15 Systems, integrable 32
Реклама
|
|
О проекте