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Brin M., Stuck G. — Introdution to dynamical system
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Название: Introdution to dynamical system
Авторы: Brin M., Stuck G.
Аннотация: This book provides a broad introduction to the subject of dynamical systems, suitable for a one or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to areas such as number theory, data storage, and internet search engines.
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Рубрика: Физика /Динамические системы /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2002
Количество страниц: 240
Добавлена в каталог: 18.05.2005
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Предметный указатель
70
192
curve 138
topology 138
138
71
209
117
138
37
108
5
215
213
211
209
98
98
163
71
9
4
4
85 87
87
80
, 118 122
, 121
-limit point 29
-limit set 29
-dense 4
-orbit 107 110
116
1
1
1
1
1
1
85
85
2
29
209
173
-limit point 28
-limit set 28
29
209
162 172
154
212
5 7
-algebra 69
56
56
7
7
3
-transversality 147
73
194
208
208
213
60
1-step SFT 56
a.e. 71
Abelian group 87
Absolutely continuous foliation 144
Absolutely continuous measure 86
Adapted metric 109
Address of a point 170
Adjacency matrix 8 56
Adler 135
Affine subspace 51
Allowed word 8
Almost every 71
Almost periodic point 30
Almost periodic set 47
Alphabet 7 54 55
Analytic function 191
Anosov diffeomorpism 108 130 141 142
Anosov diffeomorpism, topological entropy of 116
Anosov's shadowing theorem 113
Aperiodic transformation 96
Arithmetic progression 103
Atlas 138
atom 71
Attracting periodic point 192
Attracting point 9 25 173
Attractor 18 25
Attractor, Henon 25
Attractor, hyperbolic 18
Attractor, Lorenz 25
Attractor, strange 25
Automorphism of a measure space 70
Automorphism, Bernoulli 79 209
Automorphism, group 5
Average space 80 84
Average time 80 84
Axiom A 133
B(x, r) 28
Backward invariant, set 2
Base-m expansion 5
Basic set 133
Basin of attraction 25 173 192
Basin of attraction, immediate 192
Bernoulli automorphism 79 209
Bernoulli measure 79 219
Bifurcation 183
Bifurcation, codimension-one 184
Bifurcation, flip 185
Bifurcation, fold 185
Bifurcation, generic 183
Bifurcation, period-doubling 185
Bifurcation, saddle-node 185
Birkhoff ergodic theorem 82 93
Block code 55 67
Borel -algebra 71
Borel measure 71 72
Boundary of a partition 222
Bounded distortion 181
Bounded Jacobian 145
Bounded variation 160
Bowen 61 137
Branch number 192
Branch point 192
Breiman 217
C(X) 85
Cantor set 7 16 18 25 182 196 204
Ceiling function 21
Chaos 23
Chaotic behavior 23
Chaotic dynamical system 23
CHARACTER 95
Circle endomorphism 23 35 36
Circle rotation 4 35 45 95
Circle rotation, ergodicity of 77
Circle rotation, irrational 4 30 77 90
Circle rotation, irrational, is uniquely ergodic 87
CL(R) 204
Clock drift 67
Code 55
COLOR 51
Combinatorial number theory 48
Common refinement 208
Completion of a -algebra 70
Composition matrix 65
Conditional density 144
Conditional entropy 211
Conditional measure 92
Cone, stable 115
Cone, unstable 115
Conformal map 153
Conjugacy 3
Conjugacy, measure-theoretic 70
Conjugacy, topological 28 39 55
conjugate 3
Constant-length substitution 64
Continued fraction 12 91
Continuous (semi)flow 28
Continuous spectrum 95 97
Continuous-time dynamical system 2
Convergence in density 99
Convergent 91
Coordinate chart 137
Coordinate system, local 106
cov 37
Covering map 153
Critical point 192
Critical value 192
Cross-ratio 180
Cross-section, of a flow 22
Curtis 55
Cutting and stacking 96
Cvitanovic — Feigenbaum equation 189
Cylinder 54
Cylinder set 7 78
d-lim 99
deg(R) 193
Degree, of a rational map 193
Dendrite 196
Denjoy 205
Denjoy, example 161
Denjoy, theorem 160
Dense, - 4
Dense, forward orbit 32
Dense, full orbit 32
Dense, orbit 23 32
Derivative transformation 72
Deterministic dynamical system 23
Diameter 37
Diameter of a partition 218
Diffeomorphism 106
Diffeomorphism of the circle 160
Diffeomorphism, Anosov 130 141
Diffeomorphism, Axiom A 133
Diffeomorphism, group 138
Differentiable flow 107
Differentiable manifold 106 137
Differentiable map 107
Differentiable vector field 107
Differential equation 19
Dirac measure 86
Direct product 3
Directed graph 8 56 67
Discrete spectrum 94—97
Discrete-time dynamical system 1
Dist 140
Distal extension 46
Distal homeomorphism 45
Distal points 45
distribution 139
Distribution, Hoelder-continuous 143
Distribution, integrable 139
Distribution, stable 108
Distribution, unstable 108
Douady 205
Douady — Hubbard theorem 206
Doubling operator 169
Dual group 95
Dynamical system 2
Dynamical system, chaotic 23
Dynamical system, continuous-time 2
Dynamical system, deterministic 23
Dynamical system, differentiable 106
Dynamical system, ergodic 4
Dynamical system, hyperbolic 22 106
Dynamical system, minimal 4 29
Dynamical system, symbolic 54
Dynamical system, topological 28
Dynamical system, topologically mixing 33
Dynamical system, topologically transitive 31
Dynamical system,discrete-time 1
Dynamics, symbolic 6 54
Dynamics, topological 28
Edge shift 57
Elementary strong shift equivalence 62
Embedded submanifold 139
Embedding of a subshift 55
Endomorphism, expanding 5
Endomorphism, group 5
Entropy of 218
Entropy of a partition 209
Entropy of a transformation 214
Entropy, conditional 211
Entropy, horseshoe 125
Entropy, measure-theoretic 208 213 214
Entropy, metric 208 213 214
Entropy, topological 36 37 116 125
Entropy, topological, of an SFT 60
Equicontinuous extension 46
Equicontinuous homeomorphism 45
Equivalent partitions 208
Ergodic dynamical system 4
Ergodic hypothesis 69 80
Ergodic measure 86
Ergodic theorem, von Neumann 80
Ergodic theory 69
Ergodic transformation 73
Ergodicity 73 75 77
Essentially 71
Essentially invariant function 73
Essentially invariant set 73
Even system of Weiss 66
Eventually periodic point 2 171
Exceptional point 201
Exceptional set 201
Expanding endomorphism 5 30 34 107
Expanding endomorphism is mixing 77
Expanding map 5
Expansive homeomorphism 35 40
Expansive map 35
Expansive, positively 35
Expansiveness constant 35
Exponent, Hoelder 143
Exponent, Lyapunov 23
Extension 3 140
Extension, distal 46
Extension, equicontinuous 46
Extension, group 88
Extension, isometric 41 46
Extension, measure-theoretic 70
Extreme point 86
F(R) 193
f-covers 163
Factor 3 55 140
Factor map 3
Fatou 200
Fatou set 193
Fatou theorem 204
Feigenbaum constant 189
Feigenbaum phenomenon 189
Fiber 140
Fiber bundle 140
First integral 20 21
First return map 22 72
fix(f) 60
Fixed point 2
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