Renormalization and 3-manifolds which fiber over the circle:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, New Jersey
Princeton University Press
1996
|
| Series: | Annals of mathematics studies
number 142 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | vii, 253 Seiten Illustrationen, Diagramme |
| ISBN: | 9780691011530 0691011532 0691011540 |
Staff View
MARC
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| 245 | 1 | 0 | |a Renormalization and 3-manifolds which fiber over the circle |c by Curtis T. McMullen |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Introduction 1
2 Rigidity of hyperbolic manifolds 11
2.1 The Hausdorff topology 11
2.2 Manifolds and geometric limits 12
2.3 Rigidity 17
2.4 Geometric inflexibility 24
2.5 Deep points and differentiability 32
2.6 Shallow sets 34
3 Three manifolds which fiber over the circle 41
3.1 Structures on surfaces and 3 manifolds 42
3.2 Quasifuchsian groups 44
3.3 The mapping class group 46
3.4 Hyperbolic structures on mapping tori 50
3.5 Asymptotic geometry 53
3.6 Speed of algebraic convergence 60
3.7 Example: torus bundles 65
4 Quadratic maps and renormalization 75
4.1 Topologies on domains 75
4.2 Polynomials and polynomial like maps 76
4.3 The inner class 78
4.4 Improving polynomial like maps 83
4.5 Fixed points of quadratic maps 86
4.6 Renormalization 88
4.7 Simple renormalization 91
4.8 Infinite renormalization 92
5 Towers 95
5.1 Definition and basic properties 95
5.2 Infinitely renormalizable towers 97
5.3 Bounded combinatorics 99
5.4 Robustness and inner rigidity 101
v
vi Contents
5.5 Unbranched renormalizations 103
6 Rigidity of towers 105
6.1 Fine towers 106
6.2 Expansion 108
6.3 Julia sets fill the plane 112
6.4 Proof of rigidity 114
6.5 A tower is determined by its inner classes 117
7 Fixed points of renormalization 119
7.1 Framework for the construction of fixed points .... 119
7.2 Convergence of renormalization 127
7.3 Analytic continuation of the fixed point 128
7.4 Real quadratic mappings 132
8 Asymptotic structure in the Julia set 135
8.1 Rigidity and the postcritical Cantor set 135
8.2 Deep points of Julia sets 139
8.3 Small Julia sets everywhere 143
8.4 Generalized towers 149
9 Geometric limits in dynamics 151
9.1 Holomorphic relations 151
9.2 Nonlinearity and rigidity 158
9.3 Uniform twisting 164
9.4 Quadratic maps and universality 167
9.5 Speed of convergence of renormalization 170
10 Conclusion 175
Appendix A. Quasiconformal maps and flows 183
A.I Conformal structures on vector spaces 183
A.2 Maps and vector fields 186
A.3 BMO and Zygmund class 191
A.4 Compactness and modulus of continuity 196
A.5 Unique integrability 200
Contents vii
Appendix B. Visual extension 205
B.I Naturality, continuity and quasiconformality 205
B.2 Representation theory 217
B.3 The visual distortion 221
B.4 Extending quasiconformal isotopies 226
B.5 Almost isometries 232
B.6 Points of differentiability 234
B.7 Example: stretching a geodesic 237
Bibliography 241
Index 251
|
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| discipline | Mathematik |
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| id | DE-604.BV011055746 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:03:14Z |
| institution | BVB |
| isbn | 9780691011530 0691011532 0691011540 |
| language | English |
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| physical | vii, 253 Seiten Illustrationen, Diagramme |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | McMullen, Curtis T. 1958- Verfasser (DE-588)172849853 aut Renormalization and 3-manifolds which fiber over the circle by Curtis T. McMullen Princeton, New Jersey Princeton University Press 1996 © 1996 vii, 253 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies number 142 Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Dimension 3 (DE-588)4321722-9 gnd rswk-swf Renormierung (DE-588)4128419-7 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 s Dimension 3 (DE-588)4321722-9 s DE-604 Renormierung (DE-588)4128419-7 s Erscheint auch als Online-Ausgabe 978-1-4008-6517-8 Annals of mathematics studies number 142 (DE-604)BV000000991 142 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007403652&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | McMullen, Curtis T. 1958- Renormalization and 3-manifolds which fiber over the circle Annals of mathematics studies Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 3 (DE-588)4321722-9 gnd Renormierung (DE-588)4128419-7 gnd |
| subject_GND | (DE-588)4037379-4 (DE-588)4321722-9 (DE-588)4128419-7 |
| title | Renormalization and 3-manifolds which fiber over the circle |
| title_auth | Renormalization and 3-manifolds which fiber over the circle |
| title_exact_search | Renormalization and 3-manifolds which fiber over the circle |
| title_full | Renormalization and 3-manifolds which fiber over the circle by Curtis T. McMullen |
| title_fullStr | Renormalization and 3-manifolds which fiber over the circle by Curtis T. McMullen |
| title_full_unstemmed | Renormalization and 3-manifolds which fiber over the circle by Curtis T. McMullen |
| title_short | Renormalization and 3-manifolds which fiber over the circle |
| title_sort | renormalization and 3 manifolds which fiber over the circle |
| topic | Mannigfaltigkeit (DE-588)4037379-4 gnd Dimension 3 (DE-588)4321722-9 gnd Renormierung (DE-588)4128419-7 gnd |
| topic_facet | Mannigfaltigkeit Dimension 3 Renormierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007403652&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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