Metric diophantine approximation on manifolds:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
1999
|
| Series: | Cambridge tracts in mathematics
137 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 172 S. |
| ISBN: | 0521432758 |
Staff View
MARC
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| 245 | 1 | 0 | |a Metric diophantine approximation on manifolds |c V. I. Bernik ; M. M. Dodson |
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1999 | |
| 300 | |a XI, 172 S. | ||
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| 650 | 7 | |a Espaces métriques |2 ram | |
| 650 | 7 | |a Manifolds |2 gtt | |
| 650 | 4 | |a Metric spaces | |
| 650 | 7 | |a Teoria dos números |2 larpcal | |
| 650 | 7 | |a Variétés (Mathématiques) |2 ram | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Notation xi
Chapter 1. Diophantine approximation and manifolds 1
1.1. Introduction 1
1.2. Diophantine approximation in one dimension 1
1.3. Approximation in higher dimensions 5
1.4. Euclidean submanifolds 11
1.5. Metric Diophantine approximation on manifolds 19
1.6. Notes 25
Chapter 2. Khintchine s and Groshev s theorems for manifolds 27
2.1. Introduction 27
2.2. Extremal manifolds 27
2.3. Khintchine and Groshev type manifolds 29
2.4. Baker s conjecture 30
2.5. Higher dimensional manifolds 48
2.6. Notes 56
Chapter 3. Hausdorff measure and dimension 58
3.1. Introduction 58
3.2. Hausdorff measure 58
3.3. Hausdorff dimension 62
3.4. Properties of Hausdorff dimension 65
3.5. Determining the Hausdorff dimension 67
3.6. Hausdorff dimension on manifolds 73
3.7. Notes 74
Chapter 4. Upper bounds for Hausdorff dimension 77
4.1. Introduction 77
vii
viii CONTENTS
4.2. Diophantine approximation on manifolds 82
4.3. Smooth manifolds of dimension at least 2 85
4.4. Simultaneous Diophantine approximation 92
4.5. Notes 98
Chapter 5. Lower bounds for Hausdorff dimension 99
5.1. Introduction 99
5.2. Regular systems 99
5.3. Ubiquitous systems 106
5.4. Simultaneous Diophantine approximation on manifolds 117
5.5. Notes 122
Chapter 6. Diophantine approximation over the p adic field 124
6.1. Introduction to p adic numbers 124
6.2. Diophantine approximation in Qp 126
6.3. Integral polynomials with small p adic values 127
6.4. Notes 136
Chapter 7. Applications 137
7.1. Introduction 137
7.2. Diophantine type and very well approximable numbers 138
7.3. A wave equation 139
7.4. The rotation number 140
7.5. Dynamical systems 143
7.6. Linearising diffeomorphisms 148
7.7. Diophantine approximation in hyperbolic space 151
7.8. Notes 159
References 161
Index 171
|
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| indexdate | 2024-07-09T18:42:39Z |
| institution | BVB |
| isbn | 0521432758 |
| language | English |
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| physical | XI, 172 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Bernik, Vasilij I. Verfasser aut Metric diophantine approximation on manifolds V. I. Bernik ; M. M. Dodson Cambridge Cambridge Univ. Press 1999 XI, 172 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 137 Approximation diophantienne ram Aproximações diofantinas larpcal Diofantische analyse gtt Espaces métriques ram Manifolds gtt Metric spaces Teoria dos números larpcal Variétés (Mathématiques) ram Diophantine approximation Hausdorff measures Manifolds (Mathematics) (DE-588)1071861417 Konferenzschrift gnd-content Dodson, M. M. Verfasser aut Cambridge tracts in mathematics 137 (DE-604)BV000000001 137 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009038066&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bernik, Vasilij I. Dodson, M. M. Metric diophantine approximation on manifolds Cambridge tracts in mathematics Approximation diophantienne ram Aproximações diofantinas larpcal Diofantische analyse gtt Espaces métriques ram Manifolds gtt Metric spaces Teoria dos números larpcal Variétés (Mathématiques) ram Diophantine approximation Hausdorff measures Manifolds (Mathematics) |
| subject_GND | (DE-588)1071861417 |
| title | Metric diophantine approximation on manifolds |
| title_auth | Metric diophantine approximation on manifolds |
| title_exact_search | Metric diophantine approximation on manifolds |
| title_full | Metric diophantine approximation on manifolds V. I. Bernik ; M. M. Dodson |
| title_fullStr | Metric diophantine approximation on manifolds V. I. Bernik ; M. M. Dodson |
| title_full_unstemmed | Metric diophantine approximation on manifolds V. I. Bernik ; M. M. Dodson |
| title_short | Metric diophantine approximation on manifolds |
| title_sort | metric diophantine approximation on manifolds |
| topic | Approximation diophantienne ram Aproximações diofantinas larpcal Diofantische analyse gtt Espaces métriques ram Manifolds gtt Metric spaces Teoria dos números larpcal Variétés (Mathématiques) ram Diophantine approximation Hausdorff measures Manifolds (Mathematics) |
| topic_facet | Approximation diophantienne Aproximações diofantinas Diofantische analyse Espaces métriques Manifolds Metric spaces Teoria dos números Variétés (Mathématiques) Diophantine approximation Hausdorff measures Manifolds (Mathematics) Konferenzschrift |
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