Three-dimensional flows:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2010
|
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete / Folge 3
53 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIX, 358 S. Ill., graph. Darst. 235 mm x 155 mm |
| ISBN: | 9783642114137 9783642114144 |
Staff View
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| 245 | 1 | 0 | |a Three-dimensional flows |c Vítor Araújo ; Maria José Pacifico |
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| 300 | |a XIX, 358 S. |b Ill., graph. Darst. |c 235 mm x 155 mm | ||
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Record in the Search Index
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| adam_text |
XI CONTENTS 1 INTRODUCTION 1 1.1 ORGANIZATION OF THE TEXT 3 2
PRELIMINARY DEFINITIONS AND RESULTS 5 2.1 FUNDAMENTAL NOTIONS AND
DEFINITIONS 6 2.1.1 CRITICAL ELEMENTS, NON-WANDERING POINTS, STABLE AND
UNSTABLE SETS 6 2.1.2 LIMIT SETS, TRANSITIVITY, ATTRACTORS AND REPELLERS
6 2.1.3 HYPERBOLIC CRITICAL ELEMENTS 10 2.1.4 TOPOLOGICAL EQUIVALENCE,
STRUCTURAL STABILITY 10 2.2 LOW DIMENSIONAL FLOW VERSUS CHAOTIC BEHAVIOR
11 2.2.1 ONE-DIMENSIONAL FLOWS 11 2.2.2 TWO-DIMENSIONAL FLOWS 12 2.2.3
THREE DIMENSIONAL CHAOTIC ATTRACTORS 14 2.3 HYPERBOLIC FLOWS 16 2.3.1
HYPERBOLIC SETS AND SINGULARITIES 18 2.3.2 EXAMPLES OF HYPERBOLIC SETS
AND AXIOM A FLOWS 18 2.4 EXPANSIVENESS AND SENSITIVE DEPENDENCE ON
INITIAL CONDITIONS . . 21 2.4.1 CHAOTIC SYSTEMS 22 2.4.2 EXPANSIVE
SYSTEMS 24 2.5 BASIC TOOLS 27 2.5.1 THE TUBULAR FLOW THEOREM 27 2.5.2
TRANSVERSE SECTIONS AND THE POINCARE RETURN MAP 28 2.5.3 THE
HARTMAN-GROBMAN THEOREM ON LOCAL LINEARIZATION . . 28 2.5.4 THE (STRONG)
INCLINATION LEMMA (OR A-LEMMA) 29 2.5.5 HOMOCLINIC CLASSES,
TRANSITIVENESS AND DENSENESS OF PERIODIC ORBITS 30 2.5.6 THE CLOSING
LEMMA 31 2.5.7 THE CONNECTING LEMMA 31 2.5.8 THE ERGODIC CLOSING LEMMA
33 2.5.9 A PERTURBATION LEMMA FOR FLOWS 34 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1000032612 DIGITALISIERT DURCH XUE CONTENTS 2.5.10
GENERIC VECTOR FIELDS AND LYAPUNOV STABILITY 35 2.6 THE LINEAR POINCARE
FLOW 37 2.6.1 HYPERBOLIC SPLITTING FOR THE LINEAR POINCARE FLOW 37 2.6.2
DOMINATED SPLITTING FOR THE LINEAR POINCARE FLOW 39 2.6.3 INCOMPRESSIBLE
FLOWS, HYPERBOLICITY AND DOMINATED SPLITTING 43 2.7 ERGODIC THEORY 44
2.7.1 PHYSICAL OR SRB MEASURES 45 2.7.2 GIBBS MEASURES VERSUS SRB
MEASURES 47 2.8 STABILITY CONJECTURES 53 3 SINGULAR CYCLES AND ROBUST
SINGULAR ATTRACTORS 55 3.1 SINGULAR HORSESHOE 56 3.1.1 A SINGULAR
HORSESHOE MAP 56 3.1.2 A SINGULAR CYCLE WITH A SINGULAR HORSESHOE FIRST
RETURN MAP 59 3.1.3 THE SINGULAR HORSESHOE IS A PARTIALLY HYPERBOLIC SET
WITH VOLUME EXPANDING CENTRAL DIRECTION 65 3.2 BIFURCATIONS OF
SADDLE-CONNECTIONS 68 3.2.1 SADDLE-CONNECTION WITH REAL EIGENVALUES 68
3.2.2 INCLINATION FLIP AND ORBIT FLIP 69 3.2.3 SADDLE-FOCUS CONNECTION
AND SHIL'NIKOV BIFURCATIONS . 71 3.3 LORENZ ATTRACTOR AND GEOMETRIC
MODELS 73 3.3.1 PROPERTIES OF THE LORENZ SYSTEM OF EQUATIONS 74 3.3.2
THE GEOMETRIC MODEL 77 3.3.3 THE GEOMETRIC LORENZ ATTRACTOR IS A
PARTIALLY HYPERBOLIC SET WITH VOLUME EXPANDING CENTRAL DIRECTION 83
3.3.4 EXISTENCE AND ROBUSTNESS OF INVARIANT STABLE FOLIATION . 84
3.3.5 ROBUSTNESS OF THE GEOMETRIC LORENZ ATTRACTORS 93 3.3.6 THE
GEOMETRIC LORENZ ATTRACTOR IS A HOMOCLINIC CLASS . . 96 4 ROBUSTNESS ON
THE WHOLE AMBIENT SPACE 9 CONTENTS 4.3.2 UNIFORM HYPERBOLICITY FOR THE
LINEAR POINCARE FLOW ON THE WHOLE MANIFOLD 120 ROBUST TRANSITIVITY AND
SINGULAR-HYPERBOLICITY 123 5.1 DEFINITIONS AND STATEMENT OF RESULTS 124
5.1.1 EQUILIBRIA OF ROBUST ATTRACTORS ARE LORENZ-LIKE 126 5.1.2 ROBUST
ATTRACTORS ARE SINGULAR-HYPERBOLIC 127 5.1.3 BRIEF SKETCH OF THE PROOFS
128 5.2 HIGHER DIMENSIONAL ANALOGUES 129 5.2.1 SINGULAR-ATTRACTOR WITH
ARBITRARY NUMBER OF EXPANDING DIRECTIONS 129 5.2.2 THE NOTION OF
SECTIONALLY EXPANDING SETS 130 5.2.3 HOMOGENEOUS FLOWS AND SECTIONALLY
EXPANDING ATTRACTORS 130 5.3 ATTRACTORS AND ISOLATED SETS FOR C ' FLOWS
130 5.3.1 PROOF OF SUFFICIENT CONDITIONS TO OBTAIN ATTRACTORS 132 5.3.2
ROBUST SINGULAR TRANSITIVITY IMPLIES ATTRACTORS OR REPELLERS 135 5.4
ATTRACTORS AND SINGULAR-HYPERBOLICITY 142 5.4.1 UNIFORMLY DOMINATED
SPLITTING OVER THE PERIODIC ORBITS . . 144 5.4.2 DOMINATED SPLITTING
OVER A ROBUST ATTRACTOR 146 5.4.3 ROBUST ATTRACTORS ARE
SINGULAR-HYPERBOLIC 147 5.4.4 FLOW-BOXES NEAR EQUILIBRIA 150 5.4.5
UNIFORMLY BOUNDED ANGLE BETWEEN STABLE AND CENTER-UNSTABLE DIRECTIONS ON
PERIODIC ORBITS 151 SINGULAR-HYPERBOLICITY AND ROBUSTNESS 163 6.1
CROSS-SECTIONS AND POINCARE MAPS 168 6.1.1 STABLE FOLIATIONS ON
CROSS-SECTIONS 169 6.1.2 HYPERBOLICITY OF POINCARE MAPS 171 6.1.3
ADAPTED CROSS-SECTIONS 175 6.1.4 GLOBAL POINCARE RETURN MAP 180 6.1. XIV
CONTENTS 7.2.2 INFINITELY MANY COUPLED RETURNS 211 7.2.3 SEMI-GLOBAL
POINCARE MAP 212 7.2.4 A TUBE-LIKE DOMAIN WITHOUT SINGULARITIES 213
7.2.5 EVERY ORBIT LEAVES THE TUBE 215 7.2.6 THE POINCARE MAP IS
WELL-DEFINED ON EJ 216 7.2.7 EXPANSIVENESS OF THE POINCARE MAP 218 7.2.8
SINGULAR-HYPERBOLICITY AND CHAOTIC BEHAVIOR 218 7.3 NON-UNIFORM
HYPERBOLICITY 220 7.3.1 THE STARTING POINT 220 7.3.2 THE HOLDER PROPERTY
OF THE PROJECTION 221 7.3.3 INTEGRABILITY OF THE GLOBAL RETURN TIME 223
7.3.4 SUSPENDING INVARIANT MEASURES 225 7.3.5 PHYSICAL MEASURE FOR THE
GLOBAL POINCARE MAP 228 7.3.6 SUSPENSION FLOW FROM THE POINCARE MAP 229
7.3.7 PHYSICAL MEASURES FOR THE SUSPENSION 234 7.3.8 PHYSICAL MEASURE
FOR THE FLOW 234 7.3.9 HYPERBOLICITY OF THE PHYSICAL MEASURE 235 7.3.10
ABSOLUTELY CONTINUOUS DISINTEGRATION OF THE PHYSICAL MEASURE 236 7.3.11
CONSTRUCTING THE DISINTEGRATION 239 7.3.12 THE SUPPORT COVERS THE WHOLE
ATTRACTOR 247 8 SINGULAR-HYPERBOLICITY AND VOLUME 249 8.1 DOMINATED
DECOMPOSITION AND ZERO VOLUME 249 8.1.1 DOMINATED SPLITTING AND
REGULARITY 250 8.1.2 UNIFORM HYPERBOLICITY 256 8.2
SINGULAR-HYPERBOLICITY AND ZERO VOLUME 257 8.2.1 PARTIAL HYPERBOLICITY
AND ZERO VOLUME ON C 1+ FLOWS . . . 258 8.2.2 POSITIVE VOLUME VERSUS
TRANSITIVE ANOSOV FLOWS 262 8.2.3 ZERO-VOLUME FOR C 1 CONTENTS XV 10
RELATED RESULTS AND RECENT DEVELOPMENTS 309 10.1 MORE ON
SINGULAR-HYPERBOLICITY 309 10.1.1 TOPOLOGICAL DYNAMICS 309 10.1.2
ATTRACTORS THAT RESEMBLE THE LORENZ ATTRACTOR 311 10.1.3 UNFOLDING OF
SINGULAR CYCLES 312 10.1.4 CONTRACTING LORENZ-LIKE ATTRACTORS 312 10.1.5
UNFOLDING OF SINGULAR CYCLES 314 10.2 DIMENSION THEORY, ERGODIC AND
STATISTICAL PROPERTIES 314 10.2.1 LARGE DEVIATIONS FOR THE LORENZ FLOW
315 10.2.2 CENTRAL LIMIT THEOREM FOR THE LORENZ FLOW 316 10.2.3 DECAY OF
CORRELATIONS 317 10.2.4 DECAY OF CORRELATIONS FOR THE RETURN MAP AND
QUANTITATIVE RECURRENCE ON THE GEOMETRIC LORENZ FLOW 318 10.2.5
NON-MIXING FLOWS AND SLOW DECAY OF CORRELATIONS . 319 10.2.6 DECAY OF
CORRELATIONS FOR FLOWS 320 10.2.7 THERMODYNAMICAL FORMALISM 321 10.3
GENERIC CONSERVATIVE FLOWS IN DIMENSION 3 322 APPENDIX A LYAPUNOV
STABILITY ON GENERIC VECTOR FIELDS 325 APPENDIX B A PERTURBATION LEMMA
FOR FLOWS 331 APPENDIXC ROBUSTNESS OF DOMINATED DECOMPOSITION 337
REFERENCES 343 INDEX 355 |
| any_adam_object | 1 |
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| indexdate | 2024-07-20T10:41:20Z |
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| spelling | Araújo, Vítor Verfasser aut Three-dimensional flows Vítor Araújo ; Maria José Pacifico Berlin [u.a.] Springer 2010 XIX, 358 S. Ill., graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete / Folge 3 53 Kompakte Mannigfaltigkeit (DE-588)4164848-1 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Fluss Mathematik (DE-588)4489499-5 gnd rswk-swf Hyperbolizität (DE-588)4710615-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Hyperbolizität (DE-588)4710615-3 s Fluss Mathematik (DE-588)4489499-5 s Kompakte Mannigfaltigkeit (DE-588)4164848-1 s DE-604 Pacifico, Maria José Verfasser (DE-588)141839813 aut Folge 3 Ergebnisse der Mathematik und ihrer Grenzgebiete 53 (DE-604)BV000899194 53 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3423659&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=020473207&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Araújo, Vítor Pacifico, Maria José Three-dimensional flows Kompakte Mannigfaltigkeit (DE-588)4164848-1 gnd Dynamisches System (DE-588)4013396-5 gnd Fluss Mathematik (DE-588)4489499-5 gnd Hyperbolizität (DE-588)4710615-3 gnd |
| subject_GND | (DE-588)4164848-1 (DE-588)4013396-5 (DE-588)4489499-5 (DE-588)4710615-3 |
| title | Three-dimensional flows |
| title_auth | Three-dimensional flows |
| title_exact_search | Three-dimensional flows |
| title_full | Three-dimensional flows Vítor Araújo ; Maria José Pacifico |
| title_fullStr | Three-dimensional flows Vítor Araújo ; Maria José Pacifico |
| title_full_unstemmed | Three-dimensional flows Vítor Araújo ; Maria José Pacifico |
| title_short | Three-dimensional flows |
| title_sort | three dimensional flows |
| topic | Kompakte Mannigfaltigkeit (DE-588)4164848-1 gnd Dynamisches System (DE-588)4013396-5 gnd Fluss Mathematik (DE-588)4489499-5 gnd Hyperbolizität (DE-588)4710615-3 gnd |
| topic_facet | Kompakte Mannigfaltigkeit Dynamisches System Fluss Mathematik Hyperbolizität |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3423659&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020473207&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000899194 |
| work_keys_str_mv | AT araujovitor threedimensionalflows AT pacificomariajose threedimensionalflows |