Stability and bifurcation theory for non-autonomous differential equations: Cetraro, Italy 2011
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Lecture Notes in Mathematics
2065 : CIME Foundation subseries |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | IX, 303 S. graph. Darst. |
| ISBN: | 3642329055 9783642329050 |
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Record in the Search Index
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IMAGE 1
CONTENTS
THE MASLOV INDEX AND GLOBAL BIFURCATION FOR NONLINEAR BOUNDARY VALUE
PROBLEMS 1
ALBERTO BOSCAGGIN, ANNA CAPIETTO, AND WALTER DAMBROSIO 1 INTRODUCTION
AND CLASSICAL RESULTS 1
2 THE MASLOV INDEX 7
3 THE NUMBER O F MOMENTS O F VERTICALITY 12
4 THE PHASE-ANGLES AND THE NUMBER O F MOMENTS O F VERTICALITY 16
5 SOME RELATED NOTIONS 21
6 NONLINEAR FIRST ORDER SYSTEMS IN M. 2N 2 4
7 NONLINEAR DIRAC-TYPE SYSTEMS IN THE HALF-LINE 27
REFERENCES 32
DISCRETE-TIME NONAUTONOMOUS DYNAMICAL SYSTEMS 35
P.E. KLOEDEN, C. POTZSCHE, AND M. RASMUSSEN 1 INTRODUCTION 36
2 AUTONOMOUS DIFFERENCE EQUATIONS 37
2.1 AUTONOMOUS SEMIDYNAMICAL SYSTEMS 39
2.2 LYAPUNOV FUNCTIONS FOR AUTONOMOUS ATTRACTORS 4 0
3 NONAUTONOMOUS DIFFERENCE EQUATIONS 43
3.1 PROCESSES 44
3.2 SKEW-PRODUCT SYSTEMS 45
4 ATTRACTORS O F PROCESSES 50
4.1 NONAUTONOMOUS INVARIANT SETS 51
4.2 FORWARDS AND PULLBACK CONVERGENCE 52
4.3 FORWARDS AND PULLBACK ATTRACTORS 53
4.4 EXISTENCE O F PULLBACK ATTRACTORS 54
4.5 LIMITATIONS O F PULLBACK ATTRACTORS 59
5 ATTRACTORS O F SKEW-PRODUCT SYSTEMS 61
5.1 EXISTENCE O F PULLBACK ATTRACTORS 61
5.2 COMPARISON OF NONAUTONOMOUS ATTRACTORS 64
V I I
HTTP://D-NB.INFO/102462904X
IMAGE 2
VIII C O N T E N T S
5.3 LIMITATIONS O F PULLBACK ATTRACTORS REVISITED 66
5.4 LOCAL PULLBACK ATTRACTORS 68
6 LYAPUNOV FUNCTIONS 69
6.1 EXISTENCE O F A PULLBACK ABSORBING NEIGHBOURHOOD SYSTEM 70
6.2 NECESSARY AND SUFFICIENT CONDITIONS 72
7 BIFURCATIONS 79
7.1 HYPERBOLICITY AND SIMPLE EXAMPLES 80
7.2 ATTRACTOR BIFURCATION 86
7.3 SOLUTION BIFURCATION 88
8 RANDOM DYNAMICAL SYSTEMS 92
8.1 RANDOM DIFFERENCE EQUATIONS 93
8.2 RANDOM ATTRACTORS 94
8.3 RANDOM MARKOV CHAINS 96
8.4 APPROXIMATING INVARIANT MEASURES 98
REFERENCES 100
RESONANCE PROBLEMS FOR SOME NON-AUTONOMOUS ORDINARY DIFFERENTIAL
EQUATIONS 1 03
JEAN MAWHIN 1 INTRODUCTION, NOTATIONS AND PRELIMINARY RESULTS 103
1.1 INTRODUCTION 103
1.2 NOTATIONS 105
1.3 CLASSES OF HOMEOMORPHISMS 107
1.4 A NONLINEAR PROJECTOR 109
2 TOPOLOGICAL APPROACH 112
2.1 INTRODUCTION 112
2.2 DIRICHLET PROBLEM 112
2.3 PERIODIC PROBLEM 114
2.4 NEUMANN PROBLEM FOR SINGULAR 4 145
3 LAGRANGIAN VARIATIONAL APPROACH 147
3.1 INTRODUCTION 147
3.2 THE FUNCTIONAL FRAMEWORK 147
3.3 GROUND STATE SOLUTIONS 153
3.4 SADDLE POINT SOLUTIONS FOR BOUNDED NONLINEARITIES 159
3.5 MULTIPLE SOLUTIONS NEAR RESONANCE 162
3.6 BV PERIODIC SOLUTIONS O F THE FORCED PENDULUM WITH CURVATURE
OPERATOR 169
4 HAMILTONIAN VARIATIONAL APPROACH 172
4.1 INTRODUCTION 172
4.2 AN EQUIVALENT HAMILTONIAN SYSTEM AND ITS ACTION 174
4.3 MULTIPLICITY O F PERIODIC SOLUTIONS 177
REFERENCES 179
IMAGE 3
C O N T E N T S IX
NON-AUTONOMOUS FUNCTIONAL DIFFERENTIAL EQUATIONS
AND APPLICATIONS 185
SYLVIA NOVO AND RAFAEL OBAYA 1 INTRODUCTION 185
2 BASIC NOTIONS AND RESULTS 189
2.1 FLOWS OVER COMPACT METRIC SPACES 189
2.2 ALMOST PERIODIC AND ALMOST AUTOMORPHIC DYNAMICS 192
2.3 SOME IMPORTANT ODES EXAMPLES 195
2.4 ORDERED BANACH SPACES: MONOTONE SKEW-PRODUCT SEMIFLOWS 203 3
NON-AUTONOMOUS FDES WITH FINITE DELAY 206
3.1 COOPERATIVE AND IRREDUCIBLE SYSTEMS O F FINITE DELAY EQUATIONS 210
3.2 SEMICONTINUOUS EQUILIBRIA AND ALMOST AUTOMORPHIC EXTENSIONS 216 3.3
MONOTONE AND CONCAVE OR SUBLINEAR CASES 220
3.4 A NON-AUTONOMOUS CYCLIC FEEDBACK SYSTEM 225
3.5 CELLULAR NEURAL NETWORKS 229
4 NON-AUTONOMOUS CYCLIC FDES WITH INFINITE DELAY 237
4.1 STABILITY AND EXTENSIBILITY RESULTS FOR OMEGA-LIMIT SETS 237
4.2 FDES WITH INFINITE DELAY 240
4.3 MONOTONE FDES WITH INFINITE DELAY 249
4.4 COMPARTMENTAL SYSTEMS 255
REFERENCES 259
TWIST MAPPINGS WITH NON-PERIODIC ANGLES 265
MARKUS KUNZE AND RAFAEL ORTEGA 1 INTRODUCTION 265
2 SYMPLECTIC MAPS IN THE PLANE AND IN THE CYLINDER 270
3 THE TWIST CONDITION AND THE GENERATING FUNCTION 274
4 THE VARIATIONAL PRINCIPLE 277
4.1 THE FRENKEL-KONTOROWA MODEL 277
4.2 A GENERAL FRAMEWORK 278
5 EXISTENCE OF COMPLETE ORBITS 281
6 THE ACTION FUNCTIONAL O F A NEWTONIAN EQUATION 286
7 IMPACT PROBLEMS AND GENERATING FUNCTIONS 290
7.1 THE DIRICHLET PROBLEM 291
7.2 THE CONDITION O F ELASTIC BOUNCING 293
7.3 A BOUNCING BALL 294
8 COMMENTS AND BIBLIOGRAPHICAL REMARKS 296
REFERENCES 299
LIST O F PARTICIPANTS 301 |
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| discipline | Mathematik |
| format | Book |
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| spelling | Stability and bifurcation theory for non-autonomous differential equations Cetraro, Italy 2011 Anna Capietto ... Ed.: Russell Johnson ... Berlin [u.a.] Springer 2013 IX, 303 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Mathematics 2065 : CIME Foundation subseries Differentialgleichungssystem (DE-588)4121137-6 gnd rswk-swf Verzweigung Mathematik (DE-588)4078889-1 gnd rswk-swf Stabilität (DE-588)4056693-6 gnd rswk-swf Nichtautonomes System (DE-588)4480820-3 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2011 Cetraro gnd-content Differentialgleichungssystem (DE-588)4121137-6 s Nichtautonomes System (DE-588)4480820-3 s Stabilität (DE-588)4056693-6 s Verzweigung Mathematik (DE-588)4078889-1 s DE-604 Capietto, Anna 1964- Sonstige (DE-588)1031576533 oth Johnson, Russell Sonstige oth Erscheint auch als Online-Ausgabe 978-3-642-32906-7 Lecture Notes in Mathematics 2065 : CIME Foundation subseries (DE-604)BV000676446 2065 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4093451&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025497495&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stability and bifurcation theory for non-autonomous differential equations Cetraro, Italy 2011 Lecture Notes in Mathematics Differentialgleichungssystem (DE-588)4121137-6 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Stabilität (DE-588)4056693-6 gnd Nichtautonomes System (DE-588)4480820-3 gnd |
| subject_GND | (DE-588)4121137-6 (DE-588)4078889-1 (DE-588)4056693-6 (DE-588)4480820-3 (DE-588)1071861417 |
| title | Stability and bifurcation theory for non-autonomous differential equations Cetraro, Italy 2011 |
| title_auth | Stability and bifurcation theory for non-autonomous differential equations Cetraro, Italy 2011 |
| title_exact_search | Stability and bifurcation theory for non-autonomous differential equations Cetraro, Italy 2011 |
| title_full | Stability and bifurcation theory for non-autonomous differential equations Cetraro, Italy 2011 Anna Capietto ... Ed.: Russell Johnson ... |
| title_fullStr | Stability and bifurcation theory for non-autonomous differential equations Cetraro, Italy 2011 Anna Capietto ... Ed.: Russell Johnson ... |
| title_full_unstemmed | Stability and bifurcation theory for non-autonomous differential equations Cetraro, Italy 2011 Anna Capietto ... Ed.: Russell Johnson ... |
| title_short | Stability and bifurcation theory for non-autonomous differential equations |
| title_sort | stability and bifurcation theory for non autonomous differential equations cetraro italy 2011 |
| title_sub | Cetraro, Italy 2011 |
| topic | Differentialgleichungssystem (DE-588)4121137-6 gnd Verzweigung Mathematik (DE-588)4078889-1 gnd Stabilität (DE-588)4056693-6 gnd Nichtautonomes System (DE-588)4480820-3 gnd |
| topic_facet | Differentialgleichungssystem Verzweigung Mathematik Stabilität Nichtautonomes System Konferenzschrift 2011 Cetraro |
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