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
131 145 41 86 Aggregate 23 algorithmic complexity 227 246 Algorithmic complexity, density 229 Algorithmic information 226—230 Algorithmic probability 237 Algorithmically random sequence 228 Almost everywhere 87 286 Alphabet 70 Amino acids 27 Annealed average 146 Approximation 108 265 Area-preserving map see "Map" "Conservative" Arnold tongues 46 artificial intelligence 8 Attractor 41 Attractor, chaotic 42 Attractor, hyperbolic 43 Attractor, nonhyperbolic 43 Attractor, strange 41—43 Automata 166—184 Autonomous dynamical system 38 Baire category 286 Baker map 44 72 117 158 Basic word 222 224 Basin of attraction 41 48 Belousov — Zhabotinsky reaction 19 57 Benard — Marangoni convection 14 Bernoulli map 44 72 88 89 Bernoulli shift 77 81 89 120 126 271 Biological evolution 26 Biological reactions 19—21 Birkhoff's Ergodic Theorem 101 Block entropy 111 112 114 253 264 Borel measure 285 Box dimension 115 Branching ratio 252 Broadband spectra 97 Brownian motion 25 89 C-value paradox 27 Cantor set 41 45 76 116 117 153 272 273 284 Cantor set, fat 98 Cascade model 36 Cayley tree 145 Cellular automata 48—57 92 115 155 203—207 232 Cellular automata, "complex" rules 53 Cellular automata, chaotic rules 53 Cellular automata, elementary 48 Cellular automata, regular rules 51 Cellular automata, rule 20 22 30 49 54 56 90 106 107 155—157 204 258 267 Cellular automata, totalistic 49 Chaos 14 101 Chaos in cellular automata 53 106 Chaos, deterministic 38 Chaos, hyperbolic 41 Chaos, spatio-temporal 15 Chaos, temporal 13 Chaotic maps 202—203 Chaotic renormalization group see "Renormalization group chaotic" Chapman — Kolmogorov equation 91 Chemical reactions 19—21 Chomsky hierarchy 167 212 Church — Turing hypothesis 179 Circle map 45—46 Circle map, bare 45 83 88 98 Circle map, sine 45 Cluster 24 Coarse-grained entropy 246 Code 214 268 Code length 215 Code, fixed-length 215 Code, Huffman 218 Code, instantaneous 216 Code, optimal 217 Code, prefix-free 216 Code, Shannon — Fano 218 Code, uniquely decodable 215 Code, variable-length 215 223 Coding theory 214—219 233 Codon 27 Codon usage 29 Coherent light 21 complexity 103 109 212 276 Complexity and coding 219 269 Complexity, algorithmic 7 214 227 Complexity, computational 230 Complexity, discussion 211 Complexity, effective-measure 253—255 Complexity, ensemble approach 10 Complexity, forecasting 253—255 Complexity, general properties 6 263 Complexity, grammatical 214 243—245 Complexity, hierarchical scaling 214 Complexity, Kolmogorov 226 Complexity, Lempel — Ziv 233—235 Complexity, metric 264 273 Complexity, object vs subject 6 10 Complexity, product of languages 259 263 Complexity, regular-language 240—243 Complexity, scaling dynamics 262 Complexity, self-generated 9 62 249 Complexity, set 240—243 Complexity, single-item approach 10 Complexity, topological 267 Complexity, topological exponents 255—260 Complexity, tree 250 Complexity, union of languages 259 263 Compression of data 214—219 Computability 179 Conditional entropy 111 Conditional probability 90 Conjugation 81 Conjugation, topological 78 Conservative map 45 46 Conservative system 32 37 Constant-mass covering 130 235 Constant-size covering 130 Context-free languages 170—174 187—190 206 Context-free languages, stochastic 187 210 221 Context-sensitive grammar 204 Context-sensitive languages 175—177 197—198 199 206 Continuous spectrum 104 Convergence speed 254 262 264 265 Correlation dimension 150 Correlation function 96—100 148—151 185 Correlation function, mean squared 149 Cost function 64 Couette — Taylor instability 14 Critical exponents 134—141 Critical point 133 Cross-correlation 104 D0L languages 183 190—197 198 200 226 Decidability 231 Decision problem 231 defects 15 Defects, scrolls 19 Defects, spirals 19 57 Defects, vortices 19 Dense orbit 41 77 density 87 Detailed balance 58 Deterministic chaos 38 Deterministic pushdown automaton 173 Differential equations, ordinary 37—39 Differential equations, partial 33—37 Diffusion-limited aggregation 24 DIMENSION 109—118 Dimension spectrum 131 Dimension, box 115 Dimension, fractal 115 Dimension, generalized 128—131 Dimension, Hausdorff 117 Dimension, information 116 Dimension, local 287 Dimension, partial 117 288 Diophantine approximants 46 Directed graph 76 92 167 Directed percolation 57 Discrete spectrum 104 Disorder 20 22 61 Disorder, annealed 61 Disorder, quenched 61 62 Disordered systems 141—148 Dissipative, map 45 Dissipative, system 32 37 Distribution, equilibrium 91 Distribution, nonequilibrium 91 93 Diversity 249—253 DLA 24 252 DNA 26—31 100 209—211 240 domain walls 15 59 Duffing oscillator 47 Dynamical system 38 Edwards — Anderson model 61 Efficient code 215 Embedding 118 Energy cascade 17 Energy landscape 61 Ensemble average 101 entropy 59 109—118 Entropy spectrum 125 155 258 Entropy, generalized 123 Entropy, Kolmogorov — Sinai 113 Entropy, local 123 287 Entropy, metric 112 113 Entropy, properties 110 Entropy, subadditivity of 111 Entropy, topological 113 Equilibrium 12 Ergodic classification 212 Ergodic component 60 101 Ergodic shift 229 Ergodic system 87 101 102 Ergodic theory 100—109 Ergodicity, breaking 58 60 Essential frontier 97 Essential interior 97 Euler equations 35 Even system 80 Exact system 103 195 Excitable media 57 Excitable systems 20 Exons 29 100 expectation value 86 Extension of a code 215 fibonacci see "Substitution Fibonacci" Fibonacci numbers 46 Fibonacci sequence 224 244 Filtered chaotic systems 157 275 Finite automaton 167 First recurrence time 54 First-category set 107 286 Fitness 28 Flow 38 Fluid instability 13—16 Follower set 80 Forbidden word 79 83 203 Forbidden word, irreducible 79 256—260 267 290 Formal languages 79 166—184 Formal power series 188 Fractal 19 24 47 102 Fractal dimension 115 Fractal, scaling-function 276 Free energy 59 124 Free energy, Gibbs 129 Frobenius — Perron operator 93 101 104 Frustration 61 Full shift 77 Galerkin truncation 34 36 Game of life 55 206 Generalized dimension 128—131 260 Generalized entropy 123 186 260 Generalized shift 207—209 Generating partition 71 73 Genes 27 genetic code 27 Geodesic flow 82 Gibbs free energy 129 Ginzburg — Landau equation 33 Glassy phase 147 Glider 56 Golden mean 46 grammars 166—184 Grammars, production 170 Grammars, terminal symbols 170 Grammars, variable symbols 170 Greibach normal form 171 174 188 Growth matrix 191 196 Growth phenomena 23—26 Halting problem 179 Hamiltonian 120 Hamiltonian flow 95 Hamiltonian, random 142 Hausdorff dimension 117 Hausdorff measure 117 Henon map 45 152—155 262 Heteroclinic orbits 40 Hierarchical lattice 136 Hierarchical scaling 214 Hierarchy 7 17 31 60 72 92 167 214 249 270 Hoelder continuity 272 276 Homeomorphism 77 Homoclinic orbits 40 Homoclinic point 40 41 Homoclinic tangency 41 43 73 95 257 Hopf bifurcation 21 33 Horseshoe map 40 78 283 Horton — Strahler indices 252—253 Hyperbolic attractor 43 Hyperbolicity 288 Identification in the limit 219 Incompressible sequence 228 Indecomposable set 40 Indecomposable system see "Metrically transitive system" Indexed language 183 Induced map 226 Inductive inference 219 Inertial manifold 35 information 109—118 Information dimension 116 Information fluctuations 246 Information theory 212 Instabilities, fluid 13—16 Instabilities, laser 21 Instabilities, optical 21—23 Interaction spaces 122 interactions 7 58 119—123 159 260 269 Interactions, competing 61 62 Interactions, irrelevant 139 Interactions, multi-spin 121 Intermittency 89 95 221 Intermittency, spatio-temporal 15 Intermittency, type-I 95 99 151 Intermittency, weak 95 Intractability 231 Introns 29 100 Invariant measure 86 102 Invariant set 38 41 50
Реклама
function 
-limit set 
-algebra 
|
|
О проекте