Dynamical systems in cosmology:
This authoritive volume shows how modern dynamical systems theory can help us in understanding the evolution of cosmological models. It also compares this approach with Hamiltonian methods and numerical studies. A major part of the book deals with the spatially homogeneous (Bianchi) models and their...
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This authoritive volume shows how modern dynamical systems theory can help us in understanding the evolution of cosmological models. It also compares this approach with Hamiltonian methods and numerical studies. A major part of the book deals with the spatially homogeneous (Bianchi) models and their isotropic subclass, the Friedmann-Lemaitre models, but certain classes of inhomogeneous models (for example 'silent universes') are also examined. The analysis leads to an understanding of how special (high symmetry) models determine the evolution of more general families of models; and how these families relate to real cosmological observations. This is the first book to relate modern dynamical systems theory to both cosmological models and cosmological observations. It provides an invaluable reference for graduate students and researchers in relativity, cosmology and dynamical systems theory. |
| Physical Description: | XIV, 343 S. graph. Darst. |
| ISBN: | 0521554578 |
Staff View
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| 520 | 3 | |a This authoritive volume shows how modern dynamical systems theory can help us in understanding the evolution of cosmological models. It also compares this approach with Hamiltonian methods and numerical studies. A major part of the book deals with the spatially homogeneous (Bianchi) models and their isotropic subclass, the Friedmann-Lemaitre models, but certain classes of inhomogeneous models (for example 'silent universes') are also examined. The analysis leads to an understanding of how special (high symmetry) models determine the evolution of more general families of models; and how these families relate to real cosmological observations. This is the first book to relate modern dynamical systems theory to both cosmological models and cosmological observations. It provides an invaluable reference for graduate students and researchers in relativity, cosmology and dynamical systems theory. | |
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| adam_text | DYNAMICAL SYSTEMS IN COSMOLOGY EDITED BY J. WAINWRIGHT DEPARTMENT OF
APPLIED MATHEMATICS, UNIVERSITY OF WATERLOO, WATERLOO, ONTARIO N2L 3G1,
CANADA G. F. R. ELLIS DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS,
UNIVERSITY OF CAPE TOWN RONDEBOSCH 7000, SOUTH AFRICA CAMBRIDGE
UNIVERSITY PRESS CONTENTS LIST OF CONTRIBUTORS PAGE XI PREFACE XIII
INTRODUCTION 1 PART ONE: BACKGROUND 9 1 GEOMETRY OF COSMOLOGICAL MODELS
G.F.R. ELLIS, S.T.C. SIKHS AND J. WAINWRIGHT 11 1.1 COSMOLOGICAL MODELS
11 1.2 SYMMETRIES OF SPACE-TIME 20 1.3 EVOLUTION AND CONSTRAINT
EQUATIONS 27 1.4 ORTHONORMAL FRAME FORMALISM 31 1.5 BIANCHI COSMOLOGIES
35 1.6 GI COSMOLOGIES 42 2 FRIEDMANN-LEMAITRE UNIVERSES G.F.R. ELLIS AND
J. WAINWRIGHT 51 2.1 BASIC PROPERTIES AND SPECIAL SOLUTIONS 51 2.2
OBSERVATIONAL PARAMETERS 55 2.3 QUALITATIVE ANALYSIS . 58 2.4 UNIVERSES
CLOSE TO FRIEDMANN-LEMAITRE 62 3 COSMOLOGICAL OBSERVATIONS G.F.R. ELLIS
AND J. WAINWRIGHT 65 3.1 OBSERVATIONS OF DISCRETE SOURCES 65 3.2 THE
COSMIC MICROWAVE BACKGROUND RADIATION 67 3.3 BIG-BANG NUCLEOSYNTHESIS
(BBN) 73 3.4 IS THE UNIVERSE CLOSE TO FL? 77 3.5 THE BEST-FIT FL
PARAMETERS AND THE AGE PROBLEM 78 VLL VIII CONTENTS 4 INTRODUCTION TO
DYNAMICAL SYSTEMS R. TAVAKOL 84 4.1 DIFFERENTIAL EQUATIONS AND FLOWS 84
4.2 ORBITS AND INVARIANT SETS 90 4.3 BEHAVIOUR NEAR EQUILIBRIUM POINTS
94 4.4 ASYMPTOTIC EVOLUTION AND INTERMEDIATE EVOLUTION 98 PART TWO:
SPATIALLY HOMOGENEOUS COSMOLOGIES 105 5 QUALITATIVE ANALYSIS OF BIANCHI
COSMOLOGIES G.F.R. ELLIS, C. UGGLA AND J. WAINWRIGHT 107 5.1 OVERVIEW
107 5.2 EXPANSION-NORMALIZED VARIABLES 110 5.3 COSMOLOGICAL DYNAMICAL
SYSTEMS 115 6 BIANCHI COSMOLOGIES: NON-TILTED CLASS A MODELS J.
WAINWRIGHT 123 6.1 EVOLUTION EQUATIONS AND STATE SPACE 123 6.2 STABILITY
OF THE EQUILIBRIUM POINTS 129 6.3 ASYMPTOTICALLY SELF-SIMILAR MODELS 135
6.4 THE KASNER MAP AND THE MIXMASTER ATTRACTOR 143 6.5 SUMMARY X 147 7
BIANCHI COSMOLOGIES: NON-TILTED CLASS B MODELS C.G. HEWITT AND J.
WAINWRIGHT 153 7.1 THE EVOLUTION EQUATION AND STATE SPACE 153 7.2
STABILITY OF THE EQUILIBRIUM POINTS 159 7.3 ASYMPTOTIC AND INTERMEDIATE
EVOLUTION 164 7.4 SUMMARY 166 8 BIANCHI COSMOLOGIES: EXTENDING THE SCOPE
C.G.HEWITT, C. UGGLA AND J. WAINWRIGHT 170 8.1 THE EXCEPTIONAL BIANCHI
VP_ X , 9 MODELS 170 8.2 BIANCHI MODELS WITH A TWO-FLUID SOURCE 171 8.3
COSMIC NO-HAIR THEOREMS FOR BIANCHI MODELS 172 8.4 TILTED BIANCHI
MODELS 175 8.5 RECOLLAPSING MODELS 177 8.6 OTHER SOURCE TERMS:
LIMITATIONS 183 9 EXACT BIANCHI COSMOLOGIES AND STATE SPACE C.G. HEWITT,
S.T.C. SIKLOS, C. UGGLA AND J. WAINWRIGHT 186 9.1 SELF-SIMILAR PERFECT
FLUID AND VACUUM SOLUTIONS 186 9.2 EVOLVING VACUUM SOLUTIONS 195 9.3
EVOLVING NON-TILTED PERFECT FLUID SOLUTIONS 199 9.4 THE SPACE OF INITIAL
DATA 209 CONTENTS IX 10 HAMILTONIAN COSMOLOGY C. UGGLA 212 10.1 THE
HAMILTONIAN FORMULATION OF EINSTEIN S EQUATIONS 212 10.2 RELATIONSHIP
WITH THE ORTHONORMAL FRAME APPROACH 217 10.3 QUALITATIVE HAMILTONIAN
COSMOLOGY 222 11 DETERMINISTIC CHAOS AND BIANCHI COSMOLOGIES D.W. HOBILL
229 11.1 CHAOTIC DYNAMICAL SYSTEMS 230 11.2 THE METRIC APPROACH 233 11.3
HAMILTONIAN METHOD 237 11.4 EXPANSION-NORMALIZED VARIABLES 237 11.5
SUMMARY 242 PART THREE: INHOMOGENEOUS COSMOLOGIES 247 12 G2 COSMOLOGIES
C.G. HEWITT AND J. WAINWRIGHT 249 12.1 EVOLUTION EQUATIONS 250 12.2
EQUILIBRIUM POINTS: SELF-SIMILAR MODELS 254 12.3 EVOLVING MODELS: THE
SEPARABLE CLASS 259 12.4 G2 COSMOLOGIES AND THEIR SPECIALIZATIONS . 267
12.5 SUMMARY 269 13 SILENT UNIVERSES M. BRUNI, S. MATARRESE AND O.
PANTANO 271 13.1 BASIC EQUATIONS FOR SILENT UNIVERSES 272 13.2 DYNAMICAL
SYSTEMS ANALYSIS 277 13.3 PHYSICAL IMPLICATIONS 281 13.4 SUMMARY 285 14
COSMOLOGICAL DENSITY PERTURBATIONS P.K.S. DUNSBY 287 14.1 THE
GEOMETRICAL APPROACH TO DENSITY PERTURBATIONS 288 14.2 PERTURBATIONS OF
FL UNIVERSES 291 14.3 PERTURBATIONS OF BIANCHI I UNIVERSES 299 14.4
SUMMARY 303 PART FOUR: CONCLUSION 305 15 OVERVIEW G.F.R. ELLIS AND J.
WAINWRIGHT 307 15.1 COSMOLOGICAL DYNAMICAL SYSTEMS 308 15.2 BIANCHI
UNIVERSES AND OBSERVATIONS 312 15.3 INHOMOGENEOUS COSMOLOGIES 317
REFERENCES 319 SUBJECT INDEX 340
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| spelling | Dynamical systems in cosmology ed. by J. Wainwright ... 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1997 XIV, 343 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier This authoritive volume shows how modern dynamical systems theory can help us in understanding the evolution of cosmological models. It also compares this approach with Hamiltonian methods and numerical studies. A major part of the book deals with the spatially homogeneous (Bianchi) models and their isotropic subclass, the Friedmann-Lemaitre models, but certain classes of inhomogeneous models (for example 'silent universes') are also examined. The analysis leads to an understanding of how special (high symmetry) models determine the evolution of more general families of models; and how these families relate to real cosmological observations. This is the first book to relate modern dynamical systems theory to both cosmological models and cosmological observations. It provides an invaluable reference for graduate students and researchers in relativity, cosmology and dynamical systems theory. Cosmologie observationnelle Cosmologie relativiste Cosmologie ram Dynamique différentiable ram Dynamische systemen gtt Kosmologie gtt Système dynamique différentiable Mathematisches Modell Cosmology Mathematical models Differentiable dynamical systems Weltall (DE-588)4079154-3 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Weltall (DE-588)4079154-3 s Differenzierbares dynamisches System (DE-588)4137931-7 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Wainwright, John Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007573439&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dynamical systems in cosmology Cosmologie observationnelle Cosmologie relativiste Cosmologie ram Dynamique différentiable ram Dynamische systemen gtt Kosmologie gtt Système dynamique différentiable Mathematisches Modell Cosmology Mathematical models Differentiable dynamical systems Weltall (DE-588)4079154-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4079154-3 (DE-588)4137931-7 (DE-588)4114528-8 (DE-588)1071861417 |
| title | Dynamical systems in cosmology |
| title_auth | Dynamical systems in cosmology |
| title_exact_search | Dynamical systems in cosmology |
| title_full | Dynamical systems in cosmology ed. by J. Wainwright ... |
| title_fullStr | Dynamical systems in cosmology ed. by J. Wainwright ... |
| title_full_unstemmed | Dynamical systems in cosmology ed. by J. Wainwright ... |
| title_short | Dynamical systems in cosmology |
| title_sort | dynamical systems in cosmology |
| topic | Cosmologie observationnelle Cosmologie relativiste Cosmologie ram Dynamique différentiable ram Dynamische systemen gtt Kosmologie gtt Système dynamique différentiable Mathematisches Modell Cosmology Mathematical models Differentiable dynamical systems Weltall (DE-588)4079154-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Cosmologie observationnelle Cosmologie relativiste Cosmologie Dynamique différentiable Dynamische systemen Kosmologie Système dynamique différentiable Mathematisches Modell Cosmology Mathematical models Differentiable dynamical systems Weltall Differenzierbares dynamisches System Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007573439&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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