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Badii R., Politi A. — Complexity: Hierarchical structures and scaling in physics
Badii R., Politi A. — Complexity: Hierarchical structures and scaling in physics

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Название: Complexity: Hierarchical structures and scaling in physics

Авторы: 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: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 318

Добавлена в каталог: 14.02.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$f(\alpha)$ function      131 145
$\omega$-limit set      41
$\sigma$-algebra      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
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