Ruelle D. — Elements of Differentiable Dynamics and Bifurcation Theory :: Электронная библиотека попечительского совета мехмата МГУ

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Ruelle D. — Elements of Differentiable Dynamics and Bifurcation Theory

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Название: Elements of Differentiable Dynamics and Bifurcation Theory

Автор: Ruelle D.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 187

Добавлена в каталог: 29.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$C^{r}_{m}$       see also "Class $C^{r}_{m}$ "
$C^{r}_{m}$ , extension property      140 144—145
$\alpha$ -Lemma      see "Inclination lemma"
$\Omega$ -stability      43 167—168
$\Omega$ -stability, conjecture      171
$\rho$ -Pseudohyperbolic operator      137
$\varepsilon$ -Pseudo orbit      39—40
+ Transitivity      151
Anosov diffeomorphism      171
Anosov flow      171
Arnold's tongue      81
Atlas      143—144
Attracting set      38 49
Attractor      41 159—160
Attractor of dimension      1 163—164
Axiom A      154
Baire's theorem      134
Banach manifold      see "Manifold"
Banach space      135—138
Banach space, quotient      136
Basic class      40—41 118
Basic set      157—159
Basin of attraction      38 120—121
Basin of attraction, boundary      120—121
Bifurcation      see also "Specific bifurcations"
Bifurcation set      42—43
Bifurcation theory      42—44
Bifurcation with symmetry group      57
Bifurcation, global      118—122
Birkhoff's Ergodic Theorem      153
Bogoliubov — Krylov theory      154
Burst of turbulence      66—67
Cantor space      109 134—135
Cantor space, thickness      113 127—128
Catastrophe      120
Center manifold      32—35 59
Center stable and center unstable manifold      32—37 97
Center stable and center unstable theorem      32—34
Chain-recurrence      40 152
Chaos      41 66 73 85 86—87
Chart      14 143—144
Choquet theory      154
Circle, diffeomorphism      78—82 128—129
Circle, doubling map      161
Class $C^{r}_{m}$       see "Function" "Manifold" "Map" "Topology"
Closed set      132
Closing Lemma      47
Cloud Lemma      156—157 170
Codimension      15 142 145
Codimension of bifurcation      43
Compact space      133
Complementary subspaces      136
Computer-aided proof      73 122
Connected space      133
Contracting subspace      20
Contraction mapping theorem      134
Cover      see "Covering"
Covering      132—133
Critical point      13
Cvitanovic — Feigenbaum equation      71
CYCLE      119
Denjoy's theorem      81
Dense subset      133
Derivative      2 138
Diameter      134
Diffeomorphism      6
Diffeomorphism of class $C^{r}_{m}$       6 142 144
Diffeomorphism, local      20
Diffeomorphism, not time one map      53
Differential equation      9 148—150
DIMENSION      144 see "Topological
Diophantine condition      81
Direct bifurcation      61
Dynamical system with symmetry group      6
Dynamical system, Anosov      171
Dynamical system, Axiom A      153—154
Dynamical system, conservative      7 58
Dynamical system, continuous time      5
Dynamical system, discrete time      5
Dynamical system, dissipative      7 58
Dynamical system, Hamiltonian      7 58
Dynamical system, hyperbolic      see "Hyperbolicity"
Dynamical system, pre-Axiom A      160—161
Dynamical system, topology      see "Topology"
Dynamics      see also "Dynamical system" "Topological "Ergodic
Dynamics, differentiable      4
Embedding      145
Equivariance      6
Ergodic measure      152—153
Ergodic theorem      153—154
Ergodic theory      152—153
Ergodic theory of differentiable dynamical systems      87 172
Expanding map      161 163—164
Expanding subspace      20
Expansive constant      99
Expansiveness      99
Explosion      119
Family      132
Feigenbaum bifurcation      70—73
Feigenbaum map      72
Feigenbaum scenario      87
Filtrations      165—167
First return map      see "Poincare map"
First return time      16
Fixed point      13 18—22
Fixed point, $\rho$ -pseudohyperbolic      26
Fixed point, attracting      18 21
Fixed point, bifurcation      55—64
Fixed point, hyperbolic      18 21
Fixed point, phantom      66
Fixed point, repelling      18 21
Fixed point, vaguely attracting      61
Flip bifurcation      58—59 67—73
Flow      5
Flow of class $C^{r}_{m}$       6
Flow, defined by vector field      11—13 149—150
Flow, local      11
frequency      83
Frequency, locking      84—85
Function      131—132
Function of class $C^{r}_{m}$       2
Function, bijective      132
Function, compact      140—141
Function, differentiable      2 138—139 144
Function, Hoelder-continuous      2 126 138—139
Function, holomorphic      139
Function, injective      132
Function, Lipschitz      139
Function, real analytic      139
Function, smooth      see "Function differentiable"
Function, surjective      132
Fundamental neighborhood of attracting set      38 165—166
Fundamental neighborhood of hyperbolic set      103 105
Genericity      44—46 56—58 63—64
Geodesic flow      87 171
Global problem      19
Gradient      150
Gradient, flow      150
Graph      132
Graph, transform      28—30 36—37
Grobman — Hartman theorem for flows      22 53
Grobman — Hartman theorem for maps      20 53
Hausdorff dimension      113 135
Hausdorff measure      135
Hausdorff space      133
Henon attractor      41
Herman's theorem      81
Heteroclinic orbit      106
Heteroclinic point      106
Hilbert space      136

Homeomorphism      133
Homoclinic orbit      106 116—118
Homoclinic point      106
Homoclinic point, tangent      see "Homoclinic tangency"
Homoclinic point, transversal      107—110
Homoclinic tangency      110—112
Homoclinic tangency, crossed at nonzero speed      111
Homoclinic tangency, nondegenerate      111—112
Hopf bifurcation      58—59 74—87
Horseshoe      107—108
Hyperbolic Cover      94
Hyperbolic operator      137
Hyperbolic set      94—106 109
Hyperbolic set, wild      112—113
Hyperbolicity      18—19 48 see "Periodic "Normal "Hyperbolic "Nonhyperbolicity"
Hyperbolicity, approximate      95
Hyperbolicity, criterion      95 125—126
Hysteresis      44
Immersion      143 145
Implicit function theorem      142
Inclination lemma      50—52 72 107 156
Infinitely many sinks      112—114
Integral curve      11 149
Intermittency      66
Invariant probability measure      42 152—153
Inverse function theorem      141—142
Inverted bifurcation      61
Kupka — Smale theorem      46
Leray — Schauder degree      140—141
Limit point      133
Linearization      25 92 see
Local invariance      28
Local problem      19
Local product structure      99—100 104 109 154—156
Local recurrence      61
Lorenz attractor      87
Lorenz attractor, geometric      172
Manifold      1—4 143—146
Manifold of class $C^{r}_{m}$       2
Manifold, branched      163—164
Manneville — Pomeau phenomenon      66—67 85
Manneville — Pomeau scenario      86
MAP      see "Function"
Mapping      see "Function"
Markov partition      172
Measure      see "Invariant probability measure"
Metric space      134—135
Metric space, complete      134 144
Metrizable space      134
Mixing      151
Moebius band      70
Neighborhood      8 132
Newhouse theory      112
No-cycle condition      165
Nonhyperbolicity      114—115
Nonwandering set      42 151
Norm      135
Normal bundle      161
Normal form      75
Normal hyperbolicity      78 88—93 123—125
Open set      132
Operator      137—138
Orbit      13
Orientation      78
Palis — Takens' theorem      114—115
Paracompact space      133 144
Partition of unity      144
Period      13
Period doubling, bifurcation      see "Flip bifurcation"
Period doubling, cascade      see "Feigenbaum bifurcation"
Periodic orbit      13 23—24
Periodic orbit, attracting      23
Periodic orbit, bifurcation      62
Periodic orbit, hyperbolic      23
Periodic orbit, phantom      66 84
Periodic orbit, repelling      23
Periodic point      13 see
Periodic point near hyperbolic set      127
Persistence      90 96—97 103 105 113 120 160—161
Pitchfork bifurcation      56—57
Poincare map      14—18 24
Poincare map, global      17
Poincare map, local      17
Prehyperbolic set      94 104—105
PRODUCT      132 133 136 145 148
Pugh's closing Lemma      47
Quasiperiodic motion      83—86
Recurrence      42
Recurrence, local      61
Regularization      144
Relation $\succ$       39 152
Relation $\succeq$       165
Relatively compact set      133
Renormalization group      71 81
Residual set      44 134
Riemann metric      150
Roof function      18
Rotation      80
Rotation number      78—80
Ruelle — Takens scenario      86—87
Saddle      24
Saddle connection      115—116
Saddle-node bifurcation      57—58 64—67
Schauder fixed-point theorem      140—141
Section of vector bundle      148
Semiflow      5 12
Semiflow of class, $C^{r}_{m}$       6
Semiflow, local      63
Semigroup property      4
Sensitivity to initial condition      41 121 159
Separable space      133 144
Separatrix      121
SEQUENCE      132
Set      131—132
Shadowing      100—103 105—106
Shadowing lemma      101
Shift      109 161—162
Sil'nikov theory      116—117
Sink      24 see
Smale's homoclinic theorem      109—110
Small denominator      78
Smooth linearization      see "Linearization"
Solenoid      161—162
Source      25
Space      see "Set" "Specific
Special flow      18
Spectral decomposition      157
Spectrum      137—138
Sphere      3—4
Square-root law      61
Stability      164—171 see "Structural
Stability, conjecture      171
Stable and unstable dimension      158—159
Stable and unstable manifold      26—32 90—91 96—99 160
Stable and unstable manifold, global      46 48—49
Stable and unstable manifold, strong      32 91 97
Stable and unstable manifold, theorem      27—28
Stable and unstable set      50
Strange Attractor      41—42 85—86 159 162
Structural stability      42—43 170—171
Structural stability of circle diffeomorphisms      128—129
Subbundle      148
Subcritical bifurcation      61
Subharmonic bifurcation      see "Flip bifurcation"
Submanifold      15 142 145
Submersion      143
Supercritical bifurcation      61
Superstability      56
Support of measure      153
Suspension      18

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