Ratner's theorems on unipotent flows:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Chicago, Ill. [u.a.]
Univ. of Chicago Press
2005
|
| Schriftenreihe: | Chicago lectures in mathematics series
|
| Schlagwörter: | |
| Links: | http://www.gbv.de/dms/hbz/toc/ht014510985.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021134298&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XI, 203 S. graph. Darst. |
| ISBN: | 9780226539843 0226539849 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1819300143286976512 |
|---|---|
| adam_text | Contents
Abstract ix
Possible lecture schedules x
Acknowledgments xi
Chapter 1. Introduction to Ratner s Theorems 1
§1.1. What is Ratner s Orbit Closure Theorem? ¦¦• 1
§1.2. Margulis, Oppenheim, and quadratic forms •• 13
§1.3. Measure-theoretic versions of Ratner s Theorem 19
§1.4. Some applications of Ratner s Theorems ¦ • • • 25
§1.5. Polynomial divergence and shearing 31
§1.6. The Shearing Property for larger groups ¦ ¦ ¦ • 48
§1.7. Entropy and a proof for G = SL(2, R) 53
§1.8. Direction of divergence and a joinings proof • 56
§1.9. From measures to orbit closures 59
Brief history of Ratner s Theorems 62
Notes 64
References 67
Chapter 2. Introduction to Entropy 73
§2.1. Two dynamical systems 73
§2.2. Unpredictability 76
§2.3. Definition of entropy 79
§2.4. How to calculate entropy 85
§2.5. Stretching and the entropy of a translation • • 89
§2.6. Proof of the entropy estimate 94
Notes 100
References 102
vU
viii Contents
Chapter 3. Facts from Ergodic Theory 105
§3.1. Pointwise Ergodic Theorem 105
§3.2. Mautner Phenomenon 108
§3.3. Ergodic decomposition 113
§3.4. Averaging sets 116
Notes 118
References 120
Chapter 4. Facts about Algebraic Groups 123
§4.1. Algebraic groups 123
§4.2. Zariski closure 127
§4.3. Real Jordan decomposition 130
§4.4. Structure of almost-Zariski closed groups • • -135
§4.5. Chevalley s Theorem and applications 140
§4.6. Subgroups that are almost Zariski closed •••142
§4.7. Borel Density Theorem 146
§4.8. Subgroups defined over Q 151
§4.9. Appendix on Lie groups 154
Notes 160
References 163
Chapter 5. Proof of the Measure-Classification Theorem 165
§5.1. An outline of the proof 166
§5.2. Shearing and polynomial divergence 168
§5.3. Assumptions and a restatement of 5.2.4 • • • -171
§5.4. Definition of the subgroup S 173
§5.5. Two important consequences of shearing ¦¦¦178
§5.6. Comparing 5_ with5_ 180
§5.7. Completion of the proof 182
§5.8. Some precise statements 184
§5.9. How to eliminate Assumption 5.3.1 189
Notes 191
References 192
List of Notation 193
Index 197
|
| any_adam_object | 1 |
| author | Morris, Dave Witte |
| author_facet | Morris, Dave Witte |
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| author_sort | Morris, Dave Witte |
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| bvnumber | BV037220396 |
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| ctrlnum | (OCoLC)835761219 (DE-599)BVBBV037220396 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV037220396 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:46:57Z |
| institution | BVB |
| isbn | 9780226539843 0226539849 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021134298 |
| oclc_num | 835761219 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-384 |
| owner_facet | DE-355 DE-BY-UBR DE-384 |
| physical | XI, 203 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Univ. of Chicago Press |
| record_format | marc |
| series2 | Chicago lectures in mathematics series |
| spellingShingle | Morris, Dave Witte Ratner's theorems on unipotent flows Algebraische Gruppe (DE-588)4001164-1 gnd Unipotente Gruppe (DE-588)4314058-0 gnd Dynamisches System (DE-588)4013396-5 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4001164-1 (DE-588)4314058-0 (DE-588)4013396-5 (DE-588)4015246-7 |
| title | Ratner's theorems on unipotent flows |
| title_auth | Ratner's theorems on unipotent flows |
| title_exact_search | Ratner's theorems on unipotent flows |
| title_full | Ratner's theorems on unipotent flows Dave Witte Morris |
| title_fullStr | Ratner's theorems on unipotent flows Dave Witte Morris |
| title_full_unstemmed | Ratner's theorems on unipotent flows Dave Witte Morris |
| title_short | Ratner's theorems on unipotent flows |
| title_sort | ratner s theorems on unipotent flows |
| topic | Algebraische Gruppe (DE-588)4001164-1 gnd Unipotente Gruppe (DE-588)4314058-0 gnd Dynamisches System (DE-588)4013396-5 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Algebraische Gruppe Unipotente Gruppe Dynamisches System Ergodentheorie |
| url | http://www.gbv.de/dms/hbz/toc/ht014510985.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021134298&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT morrisdavewitte ratnerstheoremsonunipotentflows |