Hale J.K., Magalhaes L.T., Oliva W. — Dynamics in Infinite Dimensions :: Электронная библиотека попечительского совета мехмата МГУ

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Hale J.K., Magalhaes L.T., Oliva W. — Dynamics in Infinite Dimensions

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Название: Dynamics in Infinite Dimensions

Авторы: Hale J.K., Magalhaes L.T., Oliva W.

Аннотация:

This book presents an introduction to the geometric theory of infinite dimensional dynamical systems. Many of the fundamental results are presented for asymptotically smooth dynamical systems that have applications to functional differential equations as well as classes of dissipative partial differential equations. However, as in the earlier edition, the major emphasis is on retarded functional differential equations. This updated version also contains much material on neutral functional differential equations. The results in the earlier edition on Morse-Smale systems for maps are extended to a class of semiflows, which include retarded functional differential equations and parabolic partial differential equations.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2002

Количество страниц: 296

Добавлена в каталог: 11.06.2008

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Предметный указатель

subspace      81 89 98
Adjoint theory      189
Algebraic multiplicity      130
Anosov like      123
Attractor, compact global      75 221
Attractor, dimension of the      57
Attractor, global      8
Attractor, local      8
Attractor, stability relative to the      65
Bifurcation      65
Bogdanov — Takens singularity      137 138 161 166 167
Bounce-off point      243
Cech cohomology      62
Chafee — Infante problem      75
Change of variables, formal      145
Cohomological complexity      227
Collision      109
Collision point      41 107 118 123
Compact property      99
Cone, normal      216
Cone, quadratic      213
Conley index      227
Connection, heteroclinic      217
Connection, saddle      108
Controllability      132
Critical point, nondegenerate      229
Cycles      103
Diffeomorphism, Morse — Smale      216
Discretization      215
Discretization, semi-implicit      219
Dynamical systems, monotone      209
Eigenspace, generalized      130
Eigenvalue      130
Ejective      222
Elastic beam      77
Equation, difference      48
Equation, differential difference      134
Equation, first variational      23
Equation, formal adjoint      189
Equation, infinite delay      14
Equation, Levin — Nohel      33 67
Equation, linear variational      72 229
Equation, linearly damped wave      16
Equation, locally damped wave      10
Equation, Navier — Stokes      79
Equation, neutral      15
Equation, neutral delay differential      9
Equation, obtained by compactification      33
Equation, quasilinear parabolic      11
Equation, retarded differential delay      30
Equation, retarded functional differential      11
Equation, retarded semilinear wave      204
Equivalence, $\alpha$ -topological      102
Equivalence, topological      123
Ergodic measure      125
Essential spectrum      9
Feedback      137
Flow on center manifold      143
Flow, translational      223
Foliation, unstable      93
Formal duality      141 189
Formal series      143
Frechet category      54
Fredholm index      234
Function, hysteresis      206
Function, locally Lipschitzian      21
Function, Lyapunov      223
Functional number of zeros      108
Fundamental domain      83
Fundamental neighborhood      83
Generator, infinitesimal      129
Global $\lambda$ -lemma      89 102
Global extension      110
Global unstable foliation, compatible system      94
Hausdorff dimension      57
Henon map      164
Homoclinic orbit      167
Hopf bifurcation      39 72 149 182 194
Hopf supercritical bifurcation      73
Hutchinson equation      177
Hyperbolic measure      125
Hyperbolic periodic point      85
Hyperbolicity      109
Hyperbolicity, nonuniform      109
Hyperbolicity, persistence of      118
Hyperbolicity, uniform      109
Isotopy extension theorem      94
Jacobi matrix      212
Jacobi system      212
Jordan canonical form      132
Klein — Gordon dissipative equation      207 208
Klein — Gordon equation with delays      205
Krein — Rutman      210
Kuratowskii, measure of nonconipactness      28
Kurzweil      200 201
Kurzweil, persistence theorem      202
Lap number      217
Lifting, first      112
Lifting, second      113
Limit capacity      57
Local $\lambda$ -lemma      83
Lyapunov exponent      124
Lyapunov, functional      218
Manifold, center      134
Manifold, global unstable      82 101
Manifold, local stable      82 101
Manifold, local unstable      82 101
Manifold, stable      126
Manifold, unstable      126
Map, $\beta$ -contraction      28
Map, A-stable      82
Map, asymptotically smooth      27
Map, gradient like      81

Map, infinite dimensional      220
Map, Morse — Smale      81 89 220
Map, reversible      81
Matrix oscillatory      214
Morse decomposition      221 225
Morse set      221
Morse — Smale semiflow, A-stable      104
Negative feedback      221
NFDE on       52
NFDE on $\mathbb{R}^n$       46
NFDE on manifolds      44
Nilpotent      132
Non-resonance      146
Non-resonant terms      144
Nonlinear variation constants formula      202
Nonuniforin hyperbolicity      123
Nonuniforin, hyperbolicity      125
Nonuniformly hyperbolic, trajectory      123
Normal form      140 147 148 170
One-to-oneness      109
Operator, exponentially stable      48
Operator, focusing      217
Operator, indefinitely positive      216
Operator, linear compact      130
Orbit, complete      7
Orbit, connecting      225
Orbit, negative      7
Orbit, positive      7
oscillations      108
Period module      64
Periodic orbit, hyperbolic      230
Periodic orbit, nondegenerate      230
Periodic point      82
Perron      210
Persistence      118
Perturbation      118
phase diagram      91 104
Poincare compactification      38
Point, bifurcation      2
Point, collision      110
Point, hyperbolic fixed      111
Point, regular      124
Population dynamics      149 171
Predator-prey system      149 181
Property $\mathcal{K}$       99 110 122
Property $\mathcal{K}C^1$       100
Property $\mathcal{K}\mathcal{C}$       99
Realization      129
Realization of vector fields      134 138
Realization on a center manifold      137
Resolvent      118
Restrictions on flows of RFDE      138
Retraction,       195
Return maps, family of      114
RFDE on       31
RFDE on manifolds      19
RFDE on submanifolds of $\mathbb{R}^n$       31
RFDE, A-stable      66
RFDE, equivalent      66
RFDE, examples on manifolds      29
RFDE, infinite delay      53
Saddle      83
Sard theorem      234
Semi-equivalence, topological      123
Semiconjugacy of flow      225
Semiflow of transformations      99
Semiflow, $C^{1+\gamma}$       112
Semiflow, Morse — Smale      98 102
Semigroup,       7
Semigroup, A-stable      2
Semigroup, admissible      13
Semigroup, asymptotically compact      13
Semigroup, asymptotically smooth      12
Semigroup, collectively $\beta$ -contracting      28
Semigroup, compact dissipative      50
Semigroup, conditionally completely continuous      10
Semigroup, equivalent      2
Semigroup, point dissipative      11 50
Semigroup, strongly continuous      22
Set, $\omega$ -limit      7
Set, $\Omega$ -stable      93
Set, hyperbolic invariant      111
Set, invariant      8
Set, maximal compact invariant      8
Set, nonwandering      18 68 107 214
Set, uniformly asymptotically stable      8
Sine — Gordon equation      206
Sine — Gordon equation with delays      204
Sine — Gordon, retarded equation      207 208
Singularly perturbed delay equation      164
Sink      83
Smooth property      99 110 122
Solution, almost periodic      64
Solution, quasiperiodic      64
Solution, slowly oscillating      222
Source      83
Spectrum      130
Square and pulse waves      164
Stability theory of non-autonomous ODE      126
Stabilization      137
Strict egress point      243
Strict ingress point      243
System, -dynamical      7
System, cyclic      213
System, Morse — Smale      78 218
Theory, shape memory alloys      206
Topological A-equivalence      104
Topological boundary      84
Transversality      108 214 218
Transversality, unavoidable      218
Transverse motion      77
Wazewski principle      243
Wright equation      155
Zero number      217 22

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