Delay equations: functional-, complex-, and nonlinear analysis
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1995
|
| Schriftenreihe: | Applied mathematical sciences
110 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 534 S. graph. Darst. |
| ISBN: | 0387944168 |
Internformat
MARC
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| 245 | 1 | 0 | |a Delay equations |b functional-, complex-, and nonlinear analysis |c Odo Diekmann ... |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1995 | |
| 300 | |a XI, 534 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 110 | |
| 650 | 4 | |a Delay differential equations | |
| 650 | 0 | 7 | |a Differentialgleichung mit nacheilendem Argument |0 (DE-588)4199298-2 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Diekmann, Odo |d 1948- |e Sonstige |0 (DE-588)1031802193 |4 oth | |
| 830 | 0 | |a Applied mathematical sciences |v 110 |w (DE-604)BV000005274 |9 110 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006840067&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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Datensatz im Suchindex
| _version_ | 1804124697173950464 |
|---|---|
| adam_text | Contents
Preface v
0 Introduction and preview 1
0.1 An example of a retarded functional differential equation 1
0.2 Solution operators 3
0.3 Synopsis 5
0.4 A few remarks on history 10
1 Linear autonomous RFDE 11
1.1 Prelude: a motivated introduction to functions of
bounded variation 11
1.2 Linear autonomous RFDE and renewal equations 15
1.3 Solving renewal equations by Laplace transformation 23
1.4 Estimates for det A(z) and related quantities 28
1.5 Asymptotic behaviour for t — oo 31
1.6 Comments 35
II The shift semigroup 36
11.1 Introduction 36
11.2 The prototype problem 37
11.3 The dual space 40
11.4 The adjoint shift semigroup 41
II. 5 The adjoint generator and the sun subspace 42
11.6 The prototype system 49
11.7 Comments 50
III Linear RFDE as bounded perturbations 51
111.1 The basic idea, followed by a digression on weak* integration 51
111.2 Bounded perturbations in the sun reflexive case 54
111.3 Perturbations with finite dimensional range 64
111.4 Back to RFDE 69
viii Contents
111.5 Interpretation of the adjoint semigroup 76
111.6 Equivalent description of the dynamics 78
111.7 Complexification 80
111.8 Remarks about the non sun reflexive case 89
111.9 Comments 94
IV Spectral theory 95
IV.l Introduction 95
IV.2 Spectral decomposition for eventually compact semigroups ... 96
IV.3 Delay equations 104
IV.4 Characteristic matrices, equivalence and Jordan chains 109
IV. 5 The semigroup action on spectral subspaces for
delay equations 123
IV.6 Comments 134
V Completeness or small solutions? 135
V. 1 Introduction 135
V.2 Exponential type calculus 137
V.3 Completeness 140
V.4 Small solutions 150
V.5 Precise estimates for A(z)~1 | 158
V.6 Series expansions 166
V.7 Lower bounds and the Newton polygon 170
V.8 Noncompleteness, series expansions and examples 178
V.9 Arbitrary kernels of bounded variation 184
V.10 Comments 191
VI Inhomogeneous linear systems 193
VI.1 Introduction 193
VI.2 Decomposition in the variation of constants formula 194
VI.3 Forcing with finite dimensional range 196
VI.4 RFDE 197
VI.5 Comments 200
VII Semiflows for nonlinear systems 201
VII. 1 Introduction 201
VII.2 Semiflows 202
VII.3 Solutions to abstract integral equations 208
VII.4 Smoothness 214
VII.5 Linearization at a stationary point 222
VII.6 Autonomous RFDE 231
VII.7 Comments 241
Contents ix
VIII Behaviour near a hyperbolic equilibrium ... 242
VIII.1 Introduction 242
VIII.2 Spectral decomposition 243
VIII.3 Bounded solutions of the inhomogeneous linear equation .... 246
VIII.4 The unstable manifold 247
VIII.5 Invariant wedges and instability 253
VIII.6 The stable manifold 257
VIII.7 Comments 258
IX The center manifold 259
IX.1 Introduction 259
IX.2 Spectral decomposition 260
IX.3 Bounded solutions of the inhomogeneous linear equation .... 262
IX.4 Modification of the nonlinearity 264
IX.5 A Lipschitz center manifold 265
IX. 6 Contractions on embedded Banach spaces 267
IX.7 The center manifold is of class Ck 271
IX.8 Dynamics on and near the center manifold 276
IX.9 Parameter dependence 277
IX. 10 A double eigenvalue at zero 280
IX. 11 Comments 286
X Hopf bifurcation 287
X.I Introduction 287
X.2 The Hopf bifurcation theorem 287
X.3 The direction of bifurcation 292
X.4 Comments 301
XI Characteristic equations 302
XI. 1 Introduction: an impressionistic sketch 302
XI.2 The region of stability in a parameter plane 305
XI.3 Strips 312
XI.4 Case studies 317
XI.5 Comments 338
XII Time dependent linear systems 339
XII. 1 Introduction 339
XII.2 Evolutionary systems 340
XII.3 Time dependent linear RFDE 343
XII.4 Invariance of Xe: a counterexample and a sufficient
condition 345
XII.5 Perturbations with finite dimensional range 348
XII.6 Comments 354
x Contents
XIII Floquet Theory 355
XIII.1 Introduction 355
XIII.2 Preliminaries on periodicity and a stability result 356
XIII.3 Floquet multipliers 358
XIII.4 Floquet representation on eigenspaces 360
XIII.5 Comments 363
XIV Periodic orbits 364
XIV.1 Introduction 364
XIV. 2 The Floquet multipliers of a periodic orbit 365
XIV.3 Poincare maps 368
XIV.4 Poincare maps and Floquet multipliers 372
XIV.5 Comments 376
XV The prototype equation for delayed negative
feedback: periodic solutions 379
XV.l Delayed feedback 379
XV.2 Smoothness and oscillation of solutions 382
XV.3 Slowly oscillating solutions 385
XV.4 The a priori estimate for unstable behaviour 391
XV. 5 Slowly oscillating solutions which grow away from zero,
periodic solutions 399
XV.6 Estimates, proof of Theorem 5.5(i) and (iii) 408
XV. 7 The fixed point index for retracts in Banach spaces,
Whyburn s lemma 412
XV.8 Proof of Theorem 5.5(ii) and (iv) 415
XV.9 Comments 421
XVI On the global dynamics of nonlinear
autonomous differential delay equations .... 426
XVI.l Negative feedback 426
XVI.2 A limiting case 430
XVI.3 Chaotic dynamics in case of negative feedback 439
XVI.4 Mixed feedback 441
XVI.5 Some global results for general autonomous RFDE 442
Appendices
I Bounded variation, measure and integration 443
1.1 Functions of bounded variation 443
1.2 Abstract integration 446
Contents xi
II Introduction to the theory of strongly continuous
semigroups of bounded linear operators and
their adjoints 452
II. 1 Strongly continuous semigroups 452
11.2 Interlude: absolute continuity 458
11.3 Adjoint semigroups 460
11.4 Spectral theory and asymptotic behaviour 468
III The operational calculus 474
III. 1 Vector valued functions 474
111.2 Bounded operators 476
111.3 Unbounded operators 477
IV Smoothness of the substitution operator 482
V Tangent vectors, Banach manifolds and
transversality 492
V.I Tangent vectors of subsets of Banach spaces 492
V.2 Banach manifolds 492
V.3 Submanifolds and transversality 494
VI Fixed points of parameterized contractions 497
VII Linear age dependent population growth:
elaboration of some of the exercises 500
VIII The Hopf bifurcation theorem 505
References 514
Index 530
List of symbols 533
List of notation 533
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:49:47Z |
| institution | BVB |
| isbn | 0387944168 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006840067 |
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| physical | XI, 534 S. graph. Darst. |
| publishDate | 1995 |
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| series2 | Applied mathematical sciences |
| spelling | Delay equations functional-, complex-, and nonlinear analysis Odo Diekmann ... New York [u.a.] Springer 1995 XI, 534 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 110 Delay differential equations Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd rswk-swf Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 s DE-604 Diekmann, Odo 1948- Sonstige (DE-588)1031802193 oth Applied mathematical sciences 110 (DE-604)BV000005274 110 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006840067&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Delay equations functional-, complex-, and nonlinear analysis Applied mathematical sciences Delay differential equations Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd |
| subject_GND | (DE-588)4199298-2 |
| title | Delay equations functional-, complex-, and nonlinear analysis |
| title_auth | Delay equations functional-, complex-, and nonlinear analysis |
| title_exact_search | Delay equations functional-, complex-, and nonlinear analysis |
| title_full | Delay equations functional-, complex-, and nonlinear analysis Odo Diekmann ... |
| title_fullStr | Delay equations functional-, complex-, and nonlinear analysis Odo Diekmann ... |
| title_full_unstemmed | Delay equations functional-, complex-, and nonlinear analysis Odo Diekmann ... |
| title_short | Delay equations |
| title_sort | delay equations functional complex and nonlinear analysis |
| title_sub | functional-, complex-, and nonlinear analysis |
| topic | Delay differential equations Differentialgleichung mit nacheilendem Argument (DE-588)4199298-2 gnd |
| topic_facet | Delay differential equations Differentialgleichung mit nacheilendem Argument |
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