The ergodic theory of discrete groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Press
1989
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | London Mathematical Society: London Mathematical Society lecture note series
143 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 221 S. graph. Darst. |
| ISBN: | 0521376742 |
Internformat
MARC
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| 100 | 1 | |a Nicholls, Peter J. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The ergodic theory of discrete groups |c Peter J. Nicholls |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Press |c 1989 | |
| 300 | |a XI, 221 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society: London Mathematical Society lecture note series |v 143 | |
| 650 | 4 | |a Groupes discrets | |
| 650 | 4 | |a Théorie ergodique | |
| 650 | 7 | |a Théorie ergodique |2 ram | |
| 650 | 4 | |a Discrete groups | |
| 650 | 4 | |a Ergodic theory | |
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| 689 | 0 | 1 | |a Ergodentheorie |0 (DE-588)4015246-7 |D s |
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Datensatz im Suchindex
| _version_ | 1804116838725976064 |
|---|---|
| adam_text | CONTENTS
CHAPTER 1
Preliminaries
1.1 Area 1
1.2 The Hyperbolic Space 3
1.3 Moebius Transforms 7
1.4 Discrete Groups 15
1.5 The Orbital Counting Function 18
1.6 Convergence Questions 20
CHAPTER 2
The Limit Set
2.1 Introduction 23
2.2 The Line Transitive Set 25
2.3 The Point Transitive Set 27
2.4 The Conical Limit Set 28
2.5 The Horospherical Limit Set 37
2.6 The Dirichlet Set 39
2.7 Parabolic Fixed Points 42
CHAPTER 3
A Measure on the Limit Set
3.1 Construction of an Orbital Measure 45
3.2 Change in Base Point 49
3.3 Change of Exponent 51
3.4 Variation of Base Point and Invariance Properties 53
3.5 The Atomic Part of the Measure 57
CHAPTER 4
Conformal Densitites
4.1 Introduction 68
4.2 Uniqueness 70
4.3 Local Properties 71
x Contents
4.4 The Conical Limit Set 75
4.5 The Orbital Counting Function 79
4.6 Convex Co Compact Groups 81
4.7 Summary 87
CHAPTER 5
Hyperbolically Harmonic Functions
5.1 Introduction 89
5.2 Harmonic Measure 93
5.3 Eigenfunctions 96
CHAPTER 6
The Sphere at Infinity
6.1 Introduction 100
6.2 Action on S 102
6.3 Action on S X S 105
6.4 Action on Other Products 109
CHAPTER 7
Elementary Ergodic Theory
7.1 Introduction 113
7.2 The Continuous Case 116
7.3 Invariant Measures 126
CHAPTER 8
The Geodesic Flow
8.1 Definition 128
8.2 Basic Transitivity Properties 135
8.3 Ergodicity 140
CHAPTER 9
Geometrically Finite Groups
9.1 Introduction 147
9.2 Volume of the Line Element Space 152
9.3 Hausdorff Dimension of the Limit Set 154
CHAPTER 10
Fuchsian Groups
10.1 Introduction 161
10.2 The Upper Half Plane 162
10.3 Geodesic and Horocyclic Flows 170
10.4 The Unit Disc 174
Contents xi
10.5 Ergodicity and Mixing 182
10.6 Unique Ergodicity 189
10.7 A Lattice Point Problem 199
REFERENCES 209
INDEX OF SYMBOLS 215
INDEX 216
|
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| id | DE-604.BV002415813 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:44:52Z |
| institution | BVB |
| isbn | 0521376742 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001567804 |
| oclc_num | 20012347 |
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| physical | XI, 221 S. graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society lecture note series |
| series2 | London Mathematical Society: London Mathematical Society lecture note series |
| spelling | Nicholls, Peter J. Verfasser aut The ergodic theory of discrete groups Peter J. Nicholls 1. publ. Cambridge u.a. Cambridge Univ. Press 1989 XI, 221 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society lecture note series 143 Groupes discrets Théorie ergodique Théorie ergodique ram Discrete groups Ergodic theory Diskrete Gruppe (DE-588)4135541-6 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Diskrete Gruppe (DE-588)4135541-6 s Ergodentheorie (DE-588)4015246-7 s DE-604 London Mathematical Society: London Mathematical Society lecture note series 143 (DE-604)BV000000130 143 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001567804&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nicholls, Peter J. The ergodic theory of discrete groups London Mathematical Society: London Mathematical Society lecture note series Groupes discrets Théorie ergodique Théorie ergodique ram Discrete groups Ergodic theory Diskrete Gruppe (DE-588)4135541-6 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4135541-6 (DE-588)4015246-7 |
| title | The ergodic theory of discrete groups |
| title_auth | The ergodic theory of discrete groups |
| title_exact_search | The ergodic theory of discrete groups |
| title_full | The ergodic theory of discrete groups Peter J. Nicholls |
| title_fullStr | The ergodic theory of discrete groups Peter J. Nicholls |
| title_full_unstemmed | The ergodic theory of discrete groups Peter J. Nicholls |
| title_short | The ergodic theory of discrete groups |
| title_sort | the ergodic theory of discrete groups |
| topic | Groupes discrets Théorie ergodique Théorie ergodique ram Discrete groups Ergodic theory Diskrete Gruppe (DE-588)4135541-6 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Groupes discrets Théorie ergodique Discrete groups Ergodic theory Diskrete Gruppe Ergodentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001567804&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
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