Brin M., Stuck G. — Introdution to dynamical system :: Электронная библиотека попечительского совета мехмата МГУ

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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.

Язык:

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

$(X, \mathfrak{U}, \mu)$       70
$BA(\zeta)$       192
curve      138
topology      138
      138
$C_0(X, \mathbb{C})$       71
$d(\xi, \eta)$       209
      117
      138
      37
      108
      5
$h(T) = h_{\mu}(T)$       215
$h(T, \zeta)$       213
$H(\xi |\eta)$       211
$H(\zeta)$       209
      98
      98
$I \rightarrow J$       163
$L^p(X, \mu)$       71
$q_{\mu}$       9
$R_{\alpha}$       4
      4
      85 87
$S_f^{\infty}$       87
      80
,       118 122
$W^s_{\epsilon}(x)$ , $W^u_{\epsilon}(x)$       121
$\alpha$ -limit point      29
$\alpha$ -limit set      29
$\epsilon$ -dense      4
$\epsilon$ -orbit      107 110
$\Lambda_{\epsilon}^S, \Lambda_{\epsilon}^u$       116
$\mathbb{C}$       1
$\mathbb{N}$       1
$\mathbb{N}_0$       1
$\mathbb{Q}$       1
$\mathbb{R}$       1
$\mathbb{Z}$       1
$\mathcal{M}$       85
$\mathcal{M}_T$       85
$\mathcal{O}_f(x)$       2
$\mathcal{R}(f)$       29
$\nu$       209
$\nu_j$       173
$\omega$ -limit point      28
$\omega$ -limit set      28
$\omega_f(x)$       29
$\perp$       209
$\prec$       162 172
$\rho(f)$       154
$\rho(\xi, \eta)$       212
$\Sigma$       5 7
$\sigma$ -algebra      69
$\Sigma_A^e$       56
$\Sigma_A^v$       56
$\Sigma_m$       7
$\Sigma_m^+$       7
$\sim$       3
$\theta$ -transversality      147
$\triangle$       73
$\triangle_1$       194
$\vee$       208
$\wedge$       208
$\zeta^n$       213
$\zeta_f(z)$       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 $\sigma$ -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 $\sigma$ -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 $(n, \epsilon, f)$       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, $\epsilon$ -      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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