Oseledec multiplicative ergodic theorem for laminations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
March 2017
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
1164 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | ix, 174 Seiten |
| ISBN: | 9781470422530 |
Internformat
MARC
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| 245 | 1 | 0 | |a Oseledec multiplicative ergodic theorem for laminations |c Viêt-Anh Nguyên |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c March 2017 | |
| 300 | |a ix, 174 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v volume 246, number 1164 (3rd of 6 numbers) | |
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Datensatz im Suchindex
| _version_ | 1804177428429406208 |
|---|---|
| adam_text | Contents
Acknowledgement ix
Chapter 1. Introduction 1
Chapter 2. Background 7
2.1. (Riemannian) laminations and Laplacians 7
2.2. Covering laminations 9
2.3. Heat kernels, (weakly) harmonic measures and Standing Hypotheses 10
2.4. Brownian motion and Wiener measures without holonomy 13
2.5. Wiener measures with holonomy 15
Chapter 3. Statement of the main results 19
3.1. Multiplicative cocycles 19
3.2. First Main Theorem and applications 21
3.3. Second Main Theorem and applications 24
3.4. Plan of the proof 26
Chapter 4. Preparatory results 29
4.1. Measurability issue 29
4.2. Markov property of Brownian motion 31
Chapter 5. Leafwise Lyapunov exponents 33
Chapter 6. Splitting subbundles 41
Chapter 7. Lyapunov forward filt rat ions 47
7.1. Oseledec type theorems 47
7.2. Fibered laminations and totally invariant sets 50
7.3. Cylinder laminations and end of the proof 57
Chapter 8. Lyapunov backward filtrations 67
8.1. Extended sample-path spaces 67
8.2. Leafwise Lyapunov backward exponents and Oseledec backward type
theorem 80
Chapter 9. Proof of the main results 89
9.1. Canonical cocycles and specializations 89
9.2. A-weakly harmonic measures and splitting invariant bundles 91
9.3. First Main Theorem and Ledrappier type characterization of Lyapunov
spectrum 106
9.4. Second Main Theorem and its corollaries 112
VI
CONTENTS
APPENDICES 118
Appendix A. Measure theory for sample-path spaces 119
A.l. Multifunctions and measurable selections 119
A.2. cr-algebras: approximations and measurability 121
A.3. cr-algebra stf on a leaf 124
A.4. Holonomy maps 130
A.5. Metrizability and separability of sample-path spaces 131
A.6. The leafwise diagonal is Borel measurable 135
A.7. a-algebra ^ on a lamination 135
A.8. The cylinder laminations are Riemannian continuous-like 142
A. 9. The extended sample-path space is of full outer measure 143
Appendix B. Harmonic measure theory and ergodic theory for sample-path
spaces 147
B. l. Fibered laminations 147
B.2. Relation between a lamination and its covering lamination 159
B.3. Invariance of Wiener measures with harmonic initial distribution 159
B.4. Ergodicity of Wiener measures with ergodic harmonic initial
distribution 162
Bibliography 165
Index 167
Glossary of Notation 171
|
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| id | DE-604.BV044256173 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:47:55Z |
| institution | BVB |
| isbn | 9781470422530 |
| language | English |
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| physical | ix, 174 Seiten |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Nguyên, Viêt-Anh 1974- (DE-588)1127363921 aut Oseledec multiplicative ergodic theorem for laminations Viêt-Anh Nguyên Providence, Rhode Island American Mathematical Society March 2017 ix, 174 Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 246, number 1164 (3rd of 6 numbers) Topologischer Raum (DE-588)4137586-5 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Blätterung (DE-588)4007006-2 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Topologischer Raum (DE-588)4137586-5 s Maßtheorie (DE-588)4074626-4 s Blätterung (DE-588)4007006-2 s 1\p DE-604 Memoirs of the American Mathematical Society 1164 (DE-604)BV008000141 1164 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029661191&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nguyên, Viêt-Anh 1974- Oseledec multiplicative ergodic theorem for laminations Memoirs of the American Mathematical Society Topologischer Raum (DE-588)4137586-5 gnd Maßtheorie (DE-588)4074626-4 gnd Ergodentheorie (DE-588)4015246-7 gnd Blätterung (DE-588)4007006-2 gnd |
| subject_GND | (DE-588)4137586-5 (DE-588)4074626-4 (DE-588)4015246-7 (DE-588)4007006-2 |
| title | Oseledec multiplicative ergodic theorem for laminations |
| title_auth | Oseledec multiplicative ergodic theorem for laminations |
| title_exact_search | Oseledec multiplicative ergodic theorem for laminations |
| title_full | Oseledec multiplicative ergodic theorem for laminations Viêt-Anh Nguyên |
| title_fullStr | Oseledec multiplicative ergodic theorem for laminations Viêt-Anh Nguyên |
| title_full_unstemmed | Oseledec multiplicative ergodic theorem for laminations Viêt-Anh Nguyên |
| title_short | Oseledec multiplicative ergodic theorem for laminations |
| title_sort | oseledec multiplicative ergodic theorem for laminations |
| topic | Topologischer Raum (DE-588)4137586-5 gnd Maßtheorie (DE-588)4074626-4 gnd Ergodentheorie (DE-588)4015246-7 gnd Blätterung (DE-588)4007006-2 gnd |
| topic_facet | Topologischer Raum Maßtheorie Ergodentheorie Blätterung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029661191&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT nguyenvietanh oseledecmultiplicativeergodictheoremforlaminations |