Valls C., Barreira L. — Stability of Nonautonomous Differential Equations :: Электронная библиотека попечительского совета мехмата МГУ

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Valls C., Barreira L. — Stability of Nonautonomous Differential Equations

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Название: Stability of Nonautonomous Differential Equations

Авторы: Valls C., Barreira L.

Аннотация:

The main theme of this volume is the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. In particular, the linear variational equations are always assumed to possess a nonuniform exponential behavior, given either by the existence of a nonuniform exponential contraction or a nonuniform exponential dichotomy. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2008

Количество страниц: 285

Добавлена в каталог: 22.05.2008

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Предметный указатель

stable manifold      75 100
stable manifold      102
stable manifold      116
$X_{\alpha}$       57
$\mathcal{X}_{\alpha}$       57
Admissibility      29
angle      24 252
Backward, filtration      245
Backward, Lyapunov exponent      245
Backward, regular point      245
Basis, dual      221 236 251 256
Basis, normal      236 256
Basis, normal, for a Lyapunov exponent      256
Center manifold      171 175
Center manifold, equivariance      197 214
Center manifold, existence      173
Center manifold, reversibility      197 202
Change of coordinates, Lyapunov      246
Characterization of regularity      235 256
Characterization, stable space      110
Coefficient, Perron      237 254
Coefficient, Perron, lower bound      259
Coefficient, Perron, upper bound      259
Coefficient, regularity      221 251 254
Coefficient, regularity, lower bound      259
Coefficient, regularity, upper bound      259
Cone family      86
Cone family, invariant      86
Conjugacy for flows      145
Conjugacy for maps      146
Conjugacy, Holder regularity      145 155
Dual basis      221 236 251 256
Dual normal basis      236 256
Equation, equivariant      213
Equation, Lyapunov regular      222
Equation, negative Lyapunov exponents      241
Equation, reversible      197 199
Equivariant, center manifold      197 214
Equivariant, equation      213
Equivariant, nonautonomous equation      213
Evolution operator      19
Existence of center manifolds      173
Existence of exponential dichotomies      24 222
Existence of Lipschitz stable manifolds      56
Existence of Lipschitz unstable manifolds      71
Existence of smooth stable manifolds      120
Existence of topological conjugacies      149
Exponential dichotomy      19 24 219
Exponential dichotomy for maps      147
Exponential dichotomy, basic properties      19
Exponential dichotomy, existence      24
Exponential dichotomy, nonuniform      19 222
Exponential dichotomy, robustness      27
Exponential dichotomy, uniform      19 20
Exponential trichotomy      172
Exponential trichotomy, nonuniform      172
Faa di Bruno formula      12 119 125 126
Filtration, backward      245
Filtration, forward      244
Flow, measure-preserving      244
Forward filtration      244
Forward Lyapunov exponent      244
Forward regular point      245
Grobman — Hartman theorem      145
Grobman — Hartman theorem, nonautonomous      145
Holder, conjugacy      145 155
Holder, derivatives      129
Hyperbolic solution      59
Hyperbolic trajectory      59 77 121
Inner product, Lyapunov      246
Invariant cone family      86
Linear extension of a vector field      107
Lipschitz, manifold      57
Lipschitz, stable manifold      55 58 60 242
Lipschitz, unstable manifold      71 73
Local stable manifold      58 60 77 78
Local unstable manifold      73
Lower bound Perron coefficient      259
Lower bound regularity coefficient      226
Lyapunov, change of coordinates      246
Lyapunov, exponent      25 219—221
Lyapunov, exponent, backward      245

Lyapunov, exponent, forward      244
Lyapunov, exponent, negative      241
Lyapunov, exponent, normal basis      236
Lyapunov, inner product      246
Lyapunov, norm      83 156 246
Lyapunov, regular equation      222 251 265
Lyapunov, regular point      246
Lyapunov, regularity      219 249
Lyapunov, regularity in a Hilbert space      249
Manifold, center      171 175
Manifold, Lipschitz      57
Measure-preserving flow      244
Negative Lyapunov exponent      241
Nonautonomous equation, equivariance      213
Nonautonomous equation, reversibility      197
Nonautonomous equation, stability      265
Nonautonomous Grobman — Hartman theorem      145
Nonuniform exponential dichotomy      19
Nonuniform exponential dichotomy for maps      147 155
Nonuniform exponential dichotomy in J      20
Nonuniform exponential dichotomy, existence      222
Nonuniform exponential dichotomy, strong in J      20
Nonuniform exponential trichotomy      172
Nonuniformly hyperbolic solution      59
Nonuniformly hyperbolic trajectory      59 77 121
Nonuniformly partially hyperbolic solution      175
Norm, Lyapunov      83 156 246
Normal basis      236 256
Normal basis for a Lyapunov exponent      236 256
Perron coefficient      237 254
Reduction to a triangular matrix      232
Reduction upper triangular      252
Regular      246
Regular equation      222 251 265
Regular point      246
Regular point, backward      245
Regular point, forward      245
Regularity      219 249
Regularity, characterization      235 256
Regularity, coefficient      221 226 251 254
Regularity, coefficient, lower bound      226
Regularity, coefficient, upper bound      227
Regularity, Lyapunov      219 249
Reversibility      197
Reversibility for nonautonomous equation      197
Reversibility in center manifold      197 202
Reversible equation      197 199
Robustness      27
Smooth stable manifold      75 119 243
Smooth stable manifold in $\mathbb{R}^n$       75
Smooth stable manifold in a Banach space      119
Smooth stable manifold, existence      120
Solution, exponentially unstable      266
Space, stable      22 41 148
Space, unstable      22 41 148
Stability      267
Stability of a nonautonomous equation      265
Stable manifold      77 78
Stable manifold,       75 100
Stable manifold, Ck      102 116
Stable manifold, Lipschitz      55 56 58 60 242
Stable manifold, local      58 60 77 78
Stable manifold, smooth      75 119 243
Stable space      22 41 92 110 148
Stable space, characterization      110
Stable space, construction      92
Stable space, continuity      92
Strong exponential dichotomy for maps      155
Strong exponential dichotomy in J      20
Tangent set      95 96
Topological conjugacy      149
Triangular matrix      232
Triangular operator      252 265
Triangular reduction      232
Uniform exponential dichotomy      19 20
Unstable manifold, Lipschitz      71 73
Unstable manifold, local      73
Unstable solution      266
Unstable space      22 41 148
Upper triangular      252 265
Upper triangular, reduction      252
Vector field, linear extension      107

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