Dynamical systems and semisimple groups: an introduction
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1998
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| Series: | Cambridge tracts in mathematics
126 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | xvi, 245 Seiten |
| ISBN: | 0521591627 9780521591621 |
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| 245 | 1 | 0 | |a Dynamical systems and semisimple groups |b an introduction |c Renato Feres (Washington University in St. Louis) |
| 264 | 1 | |a Cambridge |b Cambridge University Press |c 1998 | |
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Record in the Search Index
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| adam_text | Contents
Preface page xiii
1 Topological Dynamics 1
1.1 G Spaces 1
1.2 The Orbit Space 3
1.3 Suspensions 8
1.4 Dynamical Invariants 9
1.5 Anosov Diffeomorphisms 12
2 Ergodic Theory Part I 17
2.1 Review of Measure Theory 17
2.2 Recurrence 22
2.3 Ergodicity 26
2.4 Measure Theoretic Entropy 29
3 Smooth Actions and Lie Theory 32
3.1 Vector Fields and Flows 32
3.2 Foliations 38
3.3 Lie Groups and Lie Algebras 41
3.4 Infinitesimal and Local Actions 43
3.5 The Exponential Map 45
3.6 Lie Subgroups and Homogeneous Spaces 46
3.7 Continuous Homomorphisms Are Smooth 49
3.8 Representations of Compact Groups 50
3.9 Integrating Infinitesimal Actions 52
4 Algebraic Actions 59
4.1 Affine Varieties 59
4.2 Projective Varieties 61
4.3 The Descending Chain Condition 63
ix
x Contents
4.4 Functions and Morphisms 64
4.5 Nonsingular Points 65
4.6 Real Points of Complex Varieties 67
4.7 The Ordinary Topology of a Variety 67
4.8 Homogeneous Spaces 69
4.9 Rosenlicht s Theorem 71
4.10 The Rough Structure of Algebraic Groups 74
5 The Classical Groups 77
5.1 GL(n,W), GL(n, C), and GL(n,W) 77
5.2 Automorphism Groups of Bilinear Forms 80
5.3 The Lie Algebras 86
6 Geometrie Structures 88
6.1 Principal Bundles 88
6.2 Geometrie A Structures 91
6.3 Invariant Geometrie Structures 95
6.4 The Reduction Lemmas 96
6.5 The Algebraic Hüll 100
6.6 Applications to Simple Lie Groups 107
6.7 Measures as Geometrie Structures 112
7 Semisimple Lie Groups 119
7.1 Reductive and Semisimple Lie Algebras 119
7.2 The Adjoint Group 122
7.3 The Cartan Decomposition 125
7.4 The Restricted Root Space Decomposition 129
7.5 Root Spaces for the Classical Groups 132
7.6 The Iwasawa Decomposition 136
7.7 Representationsofsl(2, C) 139
7.8 The Weyl Group 144
7.9 Generation by Centralizers 146
8 Ergodic Theory Part II 149
8.1 Invariant Measures on Coset Spaces 149
8.2 Ergodicity and Unitary Representations 154
8.3 Moore s Ergodicity Theorem 156
8.4 Birkhoff s Ergodic Theorem 162
8.5 Ergodicity of Anosov Systems 165
8.6 Amenability and Kazhdan s Property T 167
Contents xi
9 Oseledec s Theorem 174
9.1 Lyapunov Exponents 174
9.2 Products of Triangulär Matrices 179
9.3 Proofof Oseledec s Theorem 187
9.4 Nonuniform Hyperbolicity and Entropy 192
10 Rigidity Theorems 196
10.1 Straightening Sections 196
10.2 // Pairs 199
10.3 // Pairs for Centralizers 206
10.4 The Cr Rigidity Theorem 212
10.5 Contracting Subbundles 215
10.6 The Theorems of Zimmer and Margulis 221
10.7 The Lyapunov Spectrum and Entropy 224
10.8 Lattice Actions 226
Appendix A: Lattices in SL(n, R) 231
A.l SL(n,Z) 231
A.2 Cocompact Lattices 236
References 241
Index 243
|
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| indexdate | 2024-07-09T18:22:14Z |
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| isbn | 0521591627 9780521591621 |
| language | English |
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| physical | xvi, 245 Seiten |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Feres, Renato Verfasser (DE-588)141592613 aut Dynamical systems and semisimple groups an introduction Renato Feres (Washington University in St. Louis) Cambridge Cambridge University Press 1998 © 1998 xvi, 245 Seiten txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 126 Hier auch später erschienene, unveränderte Nachdrucke Dynamisches System (DE-588)4013396-5 gnd rswk-swf Halbeinfache Gruppe (DE-588)4158782-0 gnd rswk-swf Halbeinfache Gruppe (DE-588)4158782-0 s Dynamisches System (DE-588)4013396-5 s DE-604 Cambridge tracts in mathematics 126 (DE-604)BV000000001 126 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008215976&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Feres, Renato Dynamical systems and semisimple groups an introduction Cambridge tracts in mathematics Dynamisches System (DE-588)4013396-5 gnd Halbeinfache Gruppe (DE-588)4158782-0 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4158782-0 |
| title | Dynamical systems and semisimple groups an introduction |
| title_auth | Dynamical systems and semisimple groups an introduction |
| title_exact_search | Dynamical systems and semisimple groups an introduction |
| title_full | Dynamical systems and semisimple groups an introduction Renato Feres (Washington University in St. Louis) |
| title_fullStr | Dynamical systems and semisimple groups an introduction Renato Feres (Washington University in St. Louis) |
| title_full_unstemmed | Dynamical systems and semisimple groups an introduction Renato Feres (Washington University in St. Louis) |
| title_short | Dynamical systems and semisimple groups |
| title_sort | dynamical systems and semisimple groups an introduction |
| title_sub | an introduction |
| topic | Dynamisches System (DE-588)4013396-5 gnd Halbeinfache Gruppe (DE-588)4158782-0 gnd |
| topic_facet | Dynamisches System Halbeinfache Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008215976&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT feresrenato dynamicalsystemsandsemisimplegroupsanintroduction |