Dynamical systems on homogeneous spaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2000
|
| Schriftenreihe: | Translations of mathematical monographs
190 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Übers. aus dem Russ. |
| Beschreibung: | XIV, 243 S. |
| ISBN: | 0821813897 |
Internformat
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| 245 | 1 | 0 | |a Dynamical systems on homogeneous spaces |c Alexander N. Starkov |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Introduction ix
List of Notations xv
Preliminaries 1
A. Ergodic theory 1
B. Topological dynamics 6
C. Lie groups and Lie algebras 10
D. Linear algebraic groups 13
E. Finite volume spaces 16
F. Mahler s criterion 20
Chapter 1. Ergodicity and Mixing of Homogeneous Flows 23
§1. General constructions in the theory of homogeneous flows 25
§2. The Mautner phenomenon and the ergodic decomposition 29
§3. Nilpotent homogeneous flows 32
§4. Toral automorphisms and examples of solvable flows 40
§5. Construction of the semisimple splitting 49
§6. Algebraic groups and homogeneous spaces of finite volume 54
§7. Solvable homogeneous flows 60
§8. Flows on semisimple homogeneous spaces 67
§9. The Mautner phenomenon, ergodicity, and mixing in the general
case 70
§10. The ergodic decomposition 75
§11. Spectral theory of homogeneous flows 81
Chapter 2. Dynamics of Unipotent Flows 93
§12. Homecoming of unipotent trajectories 95
§13. Horospherical flows on homogeneous spaces 99
§14. The geodesic and horocycle flows on surfaces of constant negative
curvature 102
§15. Rigidity of the horocycle flow 111
§16. Classification of ergodic measures of the horocycle flow 115
§17. Classification of ergodic measures of unipotent flows 121
§18. Rigidity, quotients, and joinings of unipotent flows 127
§19. Uniform distribution of unipotent trajectories 131
§20. Various problems of convergence in the space of measures 139
vii
viii CONTENTS
Chapter 3. Dynamics of Nonunipotent Flows 147
§21. Structure of orbits, invariant sets, and ergodic measures of homo¬
geneous flows 148
§22. Multiple mixing 157
§23. Partial rigidity of quasi unipotent flows 162
§24. Topological equivalence and time changes 165
§25. Divergent and bounded trajectories 173
§26. Ergodic measures and orbit closures for actions of arbitrary sub¬
groups 179
§27. Exponential mixing 183
Chapter 4. Applications to Number Theory 189
§28. The Oppenheim Davenport conjecture 190
§29. Foundations of the theory of Diophantine approximation 199
§30. Diophantine approximation from the ergodic viewpoint 209
§31. Counting lattice points in Rn 216
References 227
Index 239
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:43:06Z |
| institution | BVB |
| isbn | 0821813897 |
| language | English |
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| physical | XIV, 243 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Math. Soc. |
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| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Starkov, Alexander N. Verfasser aut Dinamicheskie sistemy na odnorodnykh prostranstvakh Dynamical systems on homogeneous spaces Alexander N. Starkov Providence, RI American Math. Soc. 2000 XIV, 243 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 190 Übers. aus dem Russ. Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Ergodentheorie (DE-588)4015246-7 s Zahlentheorie (DE-588)4067277-3 s DE-604 Translations of mathematical monographs 190 (DE-604)BV000002394 190 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009057041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Starkov, Alexander N. Dynamical systems on homogeneous spaces Translations of mathematical monographs Zahlentheorie (DE-588)4067277-3 gnd Dynamisches System (DE-588)4013396-5 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4013396-5 (DE-588)4015246-7 |
| title | Dynamical systems on homogeneous spaces |
| title_alt | Dinamicheskie sistemy na odnorodnykh prostranstvakh |
| title_auth | Dynamical systems on homogeneous spaces |
| title_exact_search | Dynamical systems on homogeneous spaces |
| title_full | Dynamical systems on homogeneous spaces Alexander N. Starkov |
| title_fullStr | Dynamical systems on homogeneous spaces Alexander N. Starkov |
| title_full_unstemmed | Dynamical systems on homogeneous spaces Alexander N. Starkov |
| title_short | Dynamical systems on homogeneous spaces |
| title_sort | dynamical systems on homogeneous spaces |
| topic | Zahlentheorie (DE-588)4067277-3 gnd Dynamisches System (DE-588)4013396-5 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Zahlentheorie Dynamisches System Ergodentheorie |
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