Global attractors of non-autonomous dissipative dynamical systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ
World Scientific
2004
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| Schriftenreihe: | Interdisciplinary mathematical sciences
1 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXIII, 502 S. |
| ISBN: | 9812560289 |
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Datensatz im Suchindex
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| adam_text | INTERDISCLPLINAFY MATHEMATICAL GLOBAL ATTRACTORS OF NON-AUTONOMOUS
DISSIPATIVE DYNAMICAL SYSTEMS DAVID N CHEBAN STATE UNIVERSITY OF
MOLDOVA, MOLDOVA WORLD SCIENTIFIC NEWJERSEY * LONDON * SINGAPORE *
BEIJING * SHANGHAI * HONGKONG * TAIPEI * CHENNAI CONTENTS PREFACE VII
NOTATIONS XXI 1. AUTONOMOUS DYNAMICAL SYSTEMS 1 1.1 SOME NOTIONS,
NOTATIONS AND FACTS FROM THEORY OF DYNAMICAL SYSTEMS 1 1.2 LIMIT
PROPERTIES OF DYNAMICAL SYSTEMS 8 1.3 CENTER OF LEVINSON 10 1.4
DISSIPATIVE SYSTEMS ON THE LOCAL COMPACT SPACES 16 1.5 CRITERIONS OF
COMPACT DISSIPATIVITY 18 1.6 LOCAL DISSIPATIVE SYSTEMS 25 1.7 GLOBAL
ATTRACTORS 29 1.8 ON A PROBLEM OF J. HALE 33 1.9 CONNECTEDNESS OF THE
LEVINSON S CENTER 38 1.10 WEAK ATTRACTORS AND CENTER OF LEVINSON 43 1.11
ASYMPTOTIC STABILITY 47 2. NON-AUTONOMOUS DISSIPATIVE DYNAMICAL SYSTEMS
53 2.1 ON THE STABILITY OF LEVINSON S CENTER 53 2.2 THE POSITIVELY
STABLE SYSTEMS 60 2.3 BEHAVIOUR OF DISSIPATIVE DYNAMICAL SYSTEMS UNDER
HOMOMORPHISMS . 64 2.4 NON-AUTONOMOUS DYNAMICAL SYSTEMS WITH CONVERGENCE
68 2.5 TESTS FOR CONVERGENCE 79 2.6 GLOBAL ATTRACTORS OF NON-AUTONOMOUS
DYNAMICAL SYSTEMS 89 2.7 GLOBAL ATTRACTOR OF COCYCLES 93 2.8 GLOBAL
ATTRACTORS OF NON-AUTONOMOUS DYNAMICAL SYSTEM WITH MINIMAL BASE 98 2.9
HOMOGENEOUS DYNAMICAL SYSTEMS 101 XVI GLOBAL ATTRACTORS OF
NOV.-AUTONOMOUS DISSIPATIVE DYNAMICAL SYSTEMS 2.10 POWER-LAW ASYMPTOTIC
OF HOMOGENEOUS SYSTEMS 107 2.11 LINEAR SYSTEMS 113 3. ANALYTIC
DISSIPATIVE SYSTEMS 119 3.1 SKEW-PRODUCT DYNAMICAL SYSTEMS AND COCYCLES
119 3.2 C-ANALYTIC SYSTEMS 123 3.3 CONVERSE OF LYAPUNOV S THEOREM FOR
C-ANALYTIC SYSTEMS 128 3.4 ON THE STRUCTURE OF COMPACT ATTRACTING SETS
OF C-ANALYTIC SYSTEMS . . 132 3.5 DYNAMICAL SYSTEMS IN SPACES OF
SECTIONS 136 3.6 QUASI-PERIODIC SOLUTIONS 139 3.7 THE ANALOGY OF
CAMERON-JOHNSON S THEOREM 142 3.8 ALMOST PERIODIC SOLUTIONS OF THE WEAK
NONLINEAR DISSIPATIVE SYSTEMS . 145 4. THE STRUCTURE OF THE LEVINSON
CENTER OF SYSTEM WITH THE CONDITION OF THE HYPERBOLICITY 155 4.1 THE
CHAIN RECURRENT MOTIONS 155 4.2 THE SPECTRAL DECOMPOSITION OF THE
LEVINSON S CENTER 157 4.3 ONE-DIMENSIONAL SYSTEMS WITH HYPERBOLIC CENTER
159 4.4 THE DISSIPATIVE CASCADES 164 4.5 THE PERIODIC DISSIPATIVE
SYSTEMS 167 5. METHOD OF LYAPUNOV FUNCTIONS 171 5.1 CRITERIONS OF
DISSIPATIVITY IN TERM OF LYAPUNOV FUNCTIONS 171 5.2 SOME CRITERIONS OF
DISSIPATIVITY OF DIFFERENTIAL EQUATIONS 178 5.3 THEOREM OF
BARBASHIN-KRASOVSKII FOR NON-AUTONOMOUS DYNAMICAL SYSTEMS 187 5.4
EQUATIONS WITH CONVERGENCE 192 5.5 DISSIPATIVITY AND CONVERGENCE OF SOME
EQUATIONS OF 2ND AND 3RD ORDER 204 5.6 CONSTRUCTION OF LYAPUNOV FUNCTION
FOR HOMOGENEOUS SYSTEMS .... 208 5.7 DIFFERENTIABLE HOMOGENEOUS SYSTEMS
213 5.8 GLOBAL ATTRACTORS OF QUASI-HOMOGENEOUS SYSTEMS 220 6.
DISSIPATIVITY OF SOME CLASSES OF EQUATIONS 225 6.1 DIFFERENCE EQUATIONS
225 6.2 EQUATIONS WITH IMPULSE 228 6.3 CONVERGENT PERIODIC EQUATIONS
WITH IMPULSE 232 6.4 ASYMPTOTIC STABILITY OF LINEAR FUNCTIONAL
DIFFERENTIAL EQUATIONS .... 236 6.5 CONVERGENCE OF MONOTONE EVOLUTIONARY
EQUATIONS 238 6.6 GLOBAL ATTRACTORS OF NON-AUTONOMOUS LORENZ SYSTEMS 244
CONTENTS XVII 6.6.1 NON-AUTONOMOUS LORENZ SYSTEMS 245 6.6.2
NON-AUTONOMOUS DISSIPATIVE DYNAMICAL SYSTEMS AND THEIR ATTRACTORS , 248
6.6.3 ALMOST PERIODIC AND RECURRENT SOLUTIONS OF NON-AUTONOMOUS LORENZ
SYSTEMS 251 6.6.4 UNIFORM AVERAGING PRINCIPLE 253 6.6.5 GLOBAL AVERAGING
PRINCIPLE FOR THE NON-AUTONOMOUS LORENZ SYSTEMS 259 7. UPPER
SEMI-CONTINUITY OF ATTRACTORS 263 7.1 INTRODUCTION 263 7.2 MAXIMAL
COMPACT INVARIANT SETS 263 7.3 UPPER SEMI-CONTINUITY 266 7.4
CONNECTEDNESS 272 7.5 APPLICATIONS 274 7.5.1 QUASI-HOMOGENEOUS SYSTEMS
274 7.5.2 MONOTONE SYSTEMS 276 7.5.3 QUASI-LINEAR SYSTEMS 278 7.5.4
NON-AUTONOMOUSLY PERTURBED SYSTEMS 279 7.5.5 NON-AUTONOMOUS 2D
NAVIER-STOKES EQUATIONS 280 7.5.6 QUASI-LINEAR FUNCTIONAL-DIFFERENTIAL
EQUATIONS 284 8. THE RELATIONSHIP BETWEEN PULLBACK, FORWARD AND GLOBAL
ATTRACTORS 287 8.1 PULLBACK, FORWARD AND GLOBAL ATTRACTORS 288 8.2
ASYMPTOTIC STABILITY IN A-CONDENSING SEMI-DYNAMICAL SYSTEMS . . . . 294
8.3 UNIFORM PULLBACK ATTRACTORS AND GLOBAL ATTRACTORS 299 8.4 EXAMPLES
OF UNIFORM PULLBACK ATTRACTORS 300 8.4.1 PERIODIC DRIVING SYSTEMS 300
8.4.2 PULLBACK ATTRACTORS WITH SINGLETON COMPONENT SETS 302 8.4.3 DISTAL
DYNAMICAL SYSTEMS 304 9. PULLBACK ATTRACTORS OF C-ANALYTIC SYSTEMS 307
9.1 C-ANALYTIC COCYCLES 309 9.2 SOME GENERAL FACTS ABOUT NON-AUTONOMOUS
DYNAMICAL SYSTEMS .... 310 9.3 POSITIVELY UNIFORMLY STABLE COCYCLES .
314 9.4 THE COMPACT GLOBAL PULLBACK ATTRACTORS OF C-ANALYTIC COCYCLES
WITH COMPACT BASE 316 9.5 THE UNIFORM DISSIPATIVE COCYCLES WITH
NONCOMPACT BASE 319 9.6 THE COMPACT AND LOCAL DISSIPATIVE COCYCLES WITH
NONCOMPACT BASE . 323 9.7 APPLICATIONS 326 XVIII GLOBAL ATTRACTORS OF
NON-AUTONOMOUS DISSIPATIVE DYNAMICAL SYSTEMS 9.7.1 ODES 326 9.7.2
CARATHEODORY DIFFERENTIAL EQUATIONS 328 9.7.3 ODES WITH IMPULSES 329 10.
PULLBACK ATTRACTORS UNDER DISCRETIZATION 331 10.1 NON-AUTONOMOUS
DYNAMICAL SYSTEMS AND PULLBACK ATTRACTORS 333 10.2 NON-AUTONOMOUS
QUASI-LINEAR DIFFERENTIAL EQUATION 334 10.3 COCYCLE PROPERTY 338 10.4
MAIN RESULT 341 10.4.1 EXISTENCE OF AN ABSORBING SET 341 10.4.2 UPPER
SEMI-CONTINUITY OF THE PULLBACK ATTRACTOR COMPONENT SETS 344 10.4.3
UPPER SEMI-CONTINUOUS CONVERGENCE OF THE DISCRETIZED PULLBACK ATTRACTORS
345 10.4.4 UPPER SEMI-CONTINUOUS CONVERGENCE OF THE DISCRETIZED GLOBAL
ATTRACTORS 346 10.5 SINGLETON SET-VALUED PULLBACK ATTRACTOR CASE 348
10.6 APPENDIX: PROOF OF LEMMA 10.4 353 11. GLOBAL ATTRACTORS OF
NON-AUTONOMOUS NAVIER-STOKES EQUATIONS 357 11.1 NON-AUTONOMOUS
NAVIER-STOKES EQUATIONS 358 11.2 ATTRACTORS OF NON-AUTONOMOUS DYNAMICAL
SYSTEMS 367 11.3 ALMOST PERIODIC AND RECURRENT SOLUTIONS OF
NON-AUTONOMOUS NAVIER- STOKES EQUATIONS 369 11.4 UNIFORM AVERAGING FOR A
FINITE INTERVAL 374 11.5 THE GLOBAL AVERAGING PRINCIPLE FOR
NAVIER-STOKES EQUATIONS 379 12. GLOBAL ATTRACTORS OF K-MONOTONE
DYNAMICAL SYSTEMS 385 12.1 GLOBAL ATTRACTORS OF ^-MONOTONE NDS 385 12.2
ON THE STRUCTURE OF LEVINSON CENTER OF V-MONOTONE NDS 389 12.3 ALMOST
PERIODIC SOLUTIONS OF V-MONOTONE SYSTEMS 391 12.4 PULLBACK ATTRACTORS OF
F-MONOTONE NDS 394 12.5 APPLICATIONS 395 12.5.1 FINITE-DIMENSIONAL
SYSTEMS 395 12.5.2 CARATHEODORY S DIFFERENTIAL EQUATIONS 399 12.5.3 ODES
WITH IMPULSE 400 12.5.4 EVOLUTION EQUATIONS WITH MONOTONE OPERATORS 402
13. LINEAR ALMOST PERIODIC DYNAMICAL SYSTEMS 407 13.1 BOUNDED MOTIONS OF
LINEAR SYSTEMS 407 CONTENTS XIX 13.2 BOUNDED SOLUTIONS OF LINEAR
EQUATIONS 416 13.3 FINITE-DIMENSIONAL SYSTEMS 422 13.4 RELATIONSHIP
BETWEEN DIFFERENT TYPES OF STABILITY 426 13.5 LINEAR A-CONDENSING
SYSTEMS 434 13.6 EXPONENTIAL STABLE SYSTEMS 437 13.7 LINEAR SYSTEM WITH
A MINIMAL BASE 439 13.8 SOME CLASSES OF UNIFORMLY EXPONENTIALLY STABLE
EQUATIONS 441 13.9 LINEAR PERIODIC SYSTEMS 450 13.9.1 EXPONENTIAL STABLE
LINEAR PERIODIC DYNAMICAL SYSTEMS 451 13.9.2 SOME CLASSES OF LINEAR
UNIFORMLY EXPONENTIALLY STABLE PERIODIC DIFFERENTIAL EQUATIONS 456 14.
TRIANGULAR MAPS 461 14.1 TRIANGULAR MAPS AND NON-AUTONOMOUS DYNAMICAL
SYSTEMS 462 14.2 LINEAR NON-AUTONOMOUS DYNAMICAL SYSTEMS 463 14.3
QUASI-LINEAR NON-AUTONOMOUS DYNAMICAL SYSTEMS 467 14.4 GLOBAL ATTRACTORS
OF QUASI-LINEAR TRIANGULAR SYSTEMS 469 14.5 ALMOST PERIODIC AND
RECURRENT SOLUTIONS 475 14.6 PSEUDO RECURRENT SOLUTIONS 477 14.7 CHAOS
IN TRIANGULAR MAPS 478 BIBLIOGRAPHY 481 INDEX 501
|
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| discipline | Mathematik |
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| indexdate | 2024-07-09T22:02:51Z |
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| isbn | 9812560289 |
| language | English |
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| physical | XXIII, 502 S. |
| publishDate | 2004 |
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| publisher | World Scientific |
| record_format | marc |
| series | Interdisciplinary mathematical sciences |
| series2 | Interdisciplinary mathematical sciences |
| spelling | Cheban, David N. Verfasser aut Global attractors of non-autonomous dissipative dynamical systems David N. Cheban Hackensack, NJ World Scientific 2004 XXIII, 502 S. txt rdacontent n rdamedia nc rdacarrier Interdisciplinary mathematical sciences 1 Includes bibliographical references and index Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Attraktor (DE-588)4140563-8 gnd rswk-swf Attraktor (DE-588)4140563-8 s Differenzierbares dynamisches System (DE-588)4137931-7 s Differentialgleichung (DE-588)4012249-9 s 1\p DE-604 DE-604 Interdisciplinary mathematical sciences 1 (DE-604)BV035420471 1 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018577198&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cheban, David N. Global attractors of non-autonomous dissipative dynamical systems Interdisciplinary mathematical sciences Differenzierbares dynamisches System (DE-588)4137931-7 gnd Differentialgleichung (DE-588)4012249-9 gnd Attraktor (DE-588)4140563-8 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4012249-9 (DE-588)4140563-8 |
| title | Global attractors of non-autonomous dissipative dynamical systems |
| title_auth | Global attractors of non-autonomous dissipative dynamical systems |
| title_exact_search | Global attractors of non-autonomous dissipative dynamical systems |
| title_full | Global attractors of non-autonomous dissipative dynamical systems David N. Cheban |
| title_fullStr | Global attractors of non-autonomous dissipative dynamical systems David N. Cheban |
| title_full_unstemmed | Global attractors of non-autonomous dissipative dynamical systems David N. Cheban |
| title_short | Global attractors of non-autonomous dissipative dynamical systems |
| title_sort | global attractors of non autonomous dissipative dynamical systems |
| topic | Differenzierbares dynamisches System (DE-588)4137931-7 gnd Differentialgleichung (DE-588)4012249-9 gnd Attraktor (DE-588)4140563-8 gnd |
| topic_facet | Differenzierbares dynamisches System Differentialgleichung Attraktor |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018577198&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT chebandavidn globalattractorsofnonautonomousdissipativedynamicalsystems |