The real Fatou conjecture:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton Univ. Press
1998
|
| Series: | Annals of mathematics studies
144 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 148 S. Ill., graph. Darst. |
| ISBN: | 0691002576 0691002584 |
Staff View
MARC
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| 245 | 1 | 0 | |a The real Fatou conjecture |c by Jacek Graczyk and Grzegorz Świątek |
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Record in the Search Index
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| adam_text | Contents
1 Review of Concepts 3
1.1 Theory of Quadratic Polynomials 3
1.1.1 Weak hyperbolicity of quadratic polynomials . 5
1.2 Dense Hyperbolicity 6
1.2.1 Theorem and its consequences 6
1.2.2 Reduced theorem 10
1.3 Steps of the Proof of Dense Hyperbolicity 12
1.3.1 Regularly returning sets and box mappings . . 12
1.3.2 Quadratic like returns 16
1.3.3 Initial construction and geometry of inducing . 18
1.3.4 Branchwise equivalence 19
1.3.5 Pull back 22
1.3.6 Conclusion of dense hyperbolicity 24
2 Quasiconformal Gluing 25
2.1 Extendibility and Distortion 26
2.1.1 Distortion lemmas 26
2.1.2 Geodesic neighborhoods 28
2.2 Saturated Maps 30
2.3 Gluing of Saturated Maps 35
2.3.1 The main step of the construction 38
2.3.2 Proof of the reduced theorem 44
3 Polynomial Like Property 45
3.1 Domains in the Complex Plane 45
3.2 Cutting Times 47
3.2.1 Reduction to a real estimate 52
3.2.2 Proof of the real estimate 61
vii
viii Contents
4 Linear Growth of Moduli 67
4.1 Box Maps and Separation Symbols 67
4.1.1 A general outline 67
4.1.2 The growth of moduli 70
4.1.3 Separation symbols 71
4.1.4 Non close returns 75
4.1.5 Close returns 85
4.2 Conformal Roughness 87
4.2.1 Lack of roughness as regularity 89
4.2.2 Quasi invariance of roughness 95
4.3 Growth of the Separation Index 100
4.3.1 Consequences of roughness 100
4.3.2 Proof of Theorem 1.2 105
5 Quasiconformal Techniques 109
5.1 Initial Inducing 109
5.1.1 Yoccoz partition 109
5.1.2 Holomorphic motions and q.c. correspondence 112
5.2 Quasiconformal Pull back 120
5.2.1 Definition of pull back 120
5.2.2 Maximal dilatation and the pull back 124
5.3 Gluing Quasiconformal Maps 129
5.3.1 Quasiconformal mappings on ring domains . . 129
5.4 Regularity of Saturated Maps 133
5.5 Straightening Theorem 139
Bibliography 143
Index 147
|
| any_adam_object | 1 |
| author | Graczyk, Jacek Świątek, Grzegorz |
| author_facet | Graczyk, Jacek Świątek, Grzegorz |
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| dewey-ones | 516 - Geometry |
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| dewey-search | 516.3/62 |
| dewey-sort | 3516.3 262 |
| dewey-tens | 510 - Mathematics |
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| isbn | 0691002576 0691002584 |
| language | English |
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| physical | VIII, 148 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Graczyk, Jacek Verfasser aut The real Fatou conjecture by Jacek Graczyk and Grzegorz Świątek Princeton, NJ Princeton Univ. Press 1998 VIII, 148 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies 144 Application quasi-conforme Jussieu Applications (Mathématiques) Conjecture Fatou réelle Jussieu Croissance linéaire Jussieu Differentiaalmeetkunde gtt Geodeten gtt Géodésiques (Mathématiques) Géodésiques (Mathématiques) ram Polynôme quadratique Jussieu Polynômes Polynômes ram Geodesics (Mathematics) Mappings (Mathematics) Polynomials Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Polynom (DE-588)4046711-9 s DE-604 Świątek, Grzegorz Verfasser aut Annals of mathematics studies 144 (DE-604)BV000000991 144 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008365423&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Graczyk, Jacek Świątek, Grzegorz The real Fatou conjecture Annals of mathematics studies Application quasi-conforme Jussieu Applications (Mathématiques) Conjecture Fatou réelle Jussieu Croissance linéaire Jussieu Differentiaalmeetkunde gtt Geodeten gtt Géodésiques (Mathématiques) Géodésiques (Mathématiques) ram Polynôme quadratique Jussieu Polynômes Polynômes ram Geodesics (Mathematics) Mappings (Mathematics) Polynomials Differentialgeometrie (DE-588)4012248-7 gnd Polynom (DE-588)4046711-9 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4046711-9 |
| title | The real Fatou conjecture |
| title_auth | The real Fatou conjecture |
| title_exact_search | The real Fatou conjecture |
| title_full | The real Fatou conjecture by Jacek Graczyk and Grzegorz Świątek |
| title_fullStr | The real Fatou conjecture by Jacek Graczyk and Grzegorz Świątek |
| title_full_unstemmed | The real Fatou conjecture by Jacek Graczyk and Grzegorz Świątek |
| title_short | The real Fatou conjecture |
| title_sort | the real fatou conjecture |
| topic | Application quasi-conforme Jussieu Applications (Mathématiques) Conjecture Fatou réelle Jussieu Croissance linéaire Jussieu Differentiaalmeetkunde gtt Geodeten gtt Géodésiques (Mathématiques) Géodésiques (Mathématiques) ram Polynôme quadratique Jussieu Polynômes Polynômes ram Geodesics (Mathematics) Mappings (Mathematics) Polynomials Differentialgeometrie (DE-588)4012248-7 gnd Polynom (DE-588)4046711-9 gnd |
| topic_facet | Application quasi-conforme Applications (Mathématiques) Conjecture Fatou réelle Croissance linéaire Differentiaalmeetkunde Geodeten Géodésiques (Mathématiques) Polynôme quadratique Polynômes Geodesics (Mathematics) Mappings (Mathematics) Polynomials Differentialgeometrie Polynom |
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