Cheban D.N. — Global Attractors of Non-Autonomous Dissipative Dynamical Systems (Interdisciplinary Mathematical Sciences Series, Vol. 1) :: Электронная библиотека попечительского совета мехмата МГУ

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Cheban D.N. — Global Attractors of Non-Autonomous Dissipative Dynamical Systems (Interdisciplinary Mathematical Sciences Series, Vol. 1)

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Название: Global Attractors of Non-Autonomous Dissipative Dynamical Systems (Interdisciplinary Mathematical Sciences Series, Vol. 1)

Автор: Cheban D.N.

Аннотация:

Cheban (State U. of Moldova) examines abstract non-autonomous dissipative dynamical systems and their applications to differential equations within disciplines involved in studying asymptotic behavior. He begins by describing autonomous dynamic systems, then proceeds to non-autonomous dissipative dynamical systems and analytic dissipative systems. He examines the structure of the Levinson center of systems with the condition of hyperbolicity, the method of Lyapunov functions, and the dissipativity of some classes of equations. He describes the upper semi-continuity of attractors, the relationship among pullback, forward, and global attractors, and the pullback attractors of C-analytic systems and non-autonomous Navier- Stokes equations. He closes with descriptions of linear "almost periodic" dynamical systems and triangular maps.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2004

Количество страниц: 502

Добавлена в каталог: 19.06.2008

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Предметный указатель

- cocycle      451
      18
$E^+{\omega}$       310
$E^-_{\omega}$       311
      18
$V’_{\Pi} (x)$       174
$\alpha$ -condensing      295 435
$\alpha$ -condensing cocycle      299
$\alpha$ -contraction      436
$\alpha$ -limit      2
$\lambda$ -condensing      35
$\lambda$ -contraction      33
$\mathbb{C}$ -analytic dissipative dynamical system      124
$\mathbb{C}$ -analytic system      123
$\mathcal{K}$       390
$\mathfrak{M}$ -dissipative      10
$\mathfrak{M}_x$       475
$\mathfrak{M}_{\varphi}$       146
$\mathfrak{N}^+_{\omega}$       310
$\mathfrak{N}^-_{\omega}$       310
$\mathfrak{N}_{\omega}$       310
$\omega$ -limit      2
$\varepsilon > 0$ shift (almost period) of point $x \in X$       2
1-Cycle      156
A      173
Absorbing (uniformly absorbing)      270
Almost recurrent (almost periodic)      2
Asymptotic stable      3
Asymptotically $\tau$ -periodic      74
Asymptotically almost periodic      74
Asymptotically compact      31
Asymptotically recurrent      74
Asymptotically stationary      74
Attracting      3
Autonomous Lorenz systems      245
Base of extension      6
Bebutov’s dynamical system      5
Bohr’s almost periodic function      327
Bounded      36
Bounded dissipative      10
Bounded k (b)-dissipativity      11
Cascade (discrete flow)      1
Cauchy’s matrix      226
Center of Levinson      11 12
Chain recurrent      155
Chaotic      478
Cocycle      7
Collectively ( uniformly collectively) asymptotic compact      270
Collectively compact dissipative      268
Compact bounded      36
Compact dissipative      10
Compact dissipative cocycle      249
Compact k (b)-dissipative      11
Compact k (b)-dissipativity      11
Comparable in limit      74
completely continuous      30
Condensing      34
Condition (A)      70
Condition (C)      53
Condition of Ladyzhenskaya      30
Conditional $\alpha$ -contraction      436
Conditionally $\alpha$ -condensing      435
Conditionally relatively compact      310
Connectedness      38
Continuous section      67
Convergent      70
Direct product of the dynamical systems      407
Dissipativity of the equation      120
Distal      304
Dynamical system      1
Dynamical system of translations      5
Exponential dichotomy      463
Extension      6
Factor of dynamical system      6
Flow      1
Forward attractor      290
Generalized homoclinic contour      156
Global asymptotic stable      3
Global attractor      29
Global attractor of the cocycle      93
Globally asymptotically stable in the sense of Lyapunov — Barbashin      54
Group (semi-group) system      1
H-class      7 135
Homogeneous      101
Homomorphism      6

Hyperbolic      157
Hyperbolic structure      157
Indecomposable      2 38
Invariant section      67
Invariant with respect to a cocycle      290
Isomorphism      6
Jointly recurrent      408
Linear non-autonomous dynamical system      113
Linear non-homogeneous system      115
Local attractor      294 379
Local condition of Lipschitz      179
Local forward attractor      379
Local k (b)-dissipativity      11
Locally bounded      35
Locally compact      73
Locally completely continuous      16
Locally dissipative      10
Locally maximal      295
Maximal compact invariant set of cocycle      264
Maximal monotone operator      239
Measure of non-compactness of Kuratowsky      9
Metric space with segments      389
Minimal set      2
Monotone      239
Monotone operator      239
Motion      1
Multiplicator      454
Non-autonomous dynamical system      6
Non-autonomous dynamical system, generated by cocycle      7
Non-autonomous Lorenz      245
Non-autonomous Navier — Stokes equation      361
Nonlinear elliptic operator      403
Operator of monodromy      454
Orbital stable      3
Orbitally stable with respect to the non-autonomous system      54
Poincare transformation      169
Point dissipative      10
Point k (b)-dissipative      11
Point k(b)-dissipativity      11
Poisson stable      2
Positively invariant (negatively invariant, invariant)      1
Power-law asymptotic      107
Problem of J.Hale      33
Projection      463
Property (S)      43 272
Pseudo recurrent      369 477
Pullback attractor      93
Pullback dissipative      327
Quasi-minimal      165
r-cycle      156
Recurrent      2
Relation of partial order      156
Sectorial operator      358
Semi-continuous      239
Shifts dynamical system      5
Skew-product dynamical system      7
Stable (unstable) manifold      3
Stable in the sense of Poisson in the negative direction      2
Stable in the sense of Poisson in the positive direction      2
Stationary ( $\tau$ -periodic, $\tau> 0$ , $\tau \in T$ ) point      2
Stepanov almost periodic function      330
Strictly metric-convex space      389
Systems of hydrodynamic type      245
Trajectory      1
Transitive      369 478
Triangular map      462
Tubular neighborhood      189
Uniform attracting      3
Uniform forward attractor      290
Uniform pullback attractor      93
Uniform stable in the positive direction      61
Uniformly collectively compact dissipative      268
Uniformly compatible      146
Uniformly dissipative      121 320
Uniformly monotone      239
Uniformly stable in the positive direction      79
Uniformly stable in the sense of Lagrange      44
Upper semi–continuous      292
V - monotone      386
V-monotone cocycle      394
Weak attractor      16
Weakly b-dissipative      30
Weakly dissipative      16
Weakly regular      146
Whole trajectory      3

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