Complex dynamics and geometry:
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2003
|
| Schriftenreihe: | SMF/AMS texts and monographs
10 Panoramas et synthèses 8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 197 S. graph. Darst. |
| ISBN: | 082183228X |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804140505449103360 |
|---|---|
| adam_text | Contents
Holomorphic Dynamical Systems
Etienne Ghys 1
The contribution of the nineteenth century: monodromy 1
The beginning of the twentieth century: Poincaré, Painlevé, Fatou, and
Julia 3
The years 1960-1980 4
Since 1980, unification? 6
Bibliography 9
Codimension-One Holomorphic Foliations, Réduction of Singularities in Low
Dimensions, and Applications
Dominique Cerveau 11
Introduction 11
1. Examples of Foliations (with and without Singularities) 12
2. Germs of Foliations 14
3. Réduction of Singularities 16
4. Réduction of Singularities of Foliations in Dimension 2 20
5. Réduction of Singularities in Dimension 3 27
6. Application to the Existence of Séparatrices 32
7. Dimension 3 32
8. What Can We Do with the Réduction of Singularities? 32
9. Foliations of C3 That Are Reduced by Point Blow-ups; Foliations with
Very Connected Singular Locus 37
10. Other Applications 38
Bibliography 41
Riemann Surface Laminations
Etienne Ghys 43
1. Introduction 43
2. Examples 44
3. Transverse Measures, Harmonie Measures 52
4. The Gauss-Bonnet and Riemann-Roch Theorems 57
5. Uniformization of Laminations 62
6. Uniformization of Parabolic Laminations 65
7. Meromorphic Functions on Laminations 76
Bibliography 83
Dynamics of Rational Maps on Pfc
Nessim Sibony 85
Introduction 85
v
vi CONTENTS
Chapter 1. Itération of Rational Maps of Pfc 91
1.1. Définitions. Dominant Maps 91
1.2. Critical Set. Blow-up 92
1.3. Preimages of a Point 93
1.4. Indeterminacy Set. Degrees of Itérâtes. Algebraically Stable Maps. 94
1.5. Fatou Sets. Julia Sets. Normal Maps. 96
1.6. Green s Current Associated with a Meromorphic Map 97
1.7. Hôlder Continuity of the Potential of T in the Domain of Normality 100
1.8. The Current T Assigns No Mass to Analytic Sets 102
1.9. The Non-Algebraically Stable Case 103
1.10. Convergence in Mean to T 104
Chapter 2. Polynomial Automorphisms of Ch 109
2.1. Introduction 109
2.2. Regular Automorphisms of Cfc 110
2.3. Relation between the Degrees of / and f~x. Periodic Points. Entropy. 116
2.4. Basins of Attraction. Stable Manifolds 119
2.5. The Invariant Currents 7^. and T T3 123
2.6. Convergence to T+ and Density of Stable Manifolds 126
2.7. Mixing Whendim/_ =0 128
Chapter 3. Holomorphic Endomorphisms of Pfe 131
3.1. Some Examples 131
3.2. Fatou Components 132
3.3. The Currents T1 (1 £ k) and Their Supports Je 136
3.4. Dynamic Hyperbolicity 138
3.5. Convergence to T 139
3.6. The Measure x. Mixing 141
3.7. Lyapunov Exponents and the Measure fj, 144
Appendix 146
A.l. Plurisubharmonic Functions. A Convergence Theorem. Jensen s
Formula 146
A.2. Plurisubharmonic (p.s.h.) Functions. Pluripolar Sets 147
A.3. Currents 148
A.4. Positive Currents on Complex Manifolds 150
A.5. Currents of Bidegree (1,1) on Pfc 152
A.6. Exterior Product of Currents 154
A.7. Pullbacks of Closed Positive Currents 155
A.8. Logarithmic Capacity in C 157
A.9. Bedford-Taylor Capacity and the Siciak Extremal Function 158
A. 10. The Dirichlet Problem for the Monge-Ampère Equation 159
Bibliography 163
Dynamics of Quadratic Polynomials
Jean-Christophe Yoccoz, notes by Marguerite Flexor 167
Introduction 167
1. General Overview 169
2. Hyperbolic Aspects 177
3. Quasiperiodic Aspects 188
Bibliography 197
|
| any_adam_object | 1 |
| author2 | Cerveau, Dominique |
| author2_role | ctb |
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| author_facet | Cerveau, Dominique |
| building | Verbundindex |
| bvnumber | BV024507212 |
| classification_rvk | SK 750 |
| ctrlnum | (OCoLC)727737772 (DE-599)BVBBV024507212 |
| dewey-full | 514.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.74 |
| dewey-search | 514.74 |
| dewey-sort | 3514.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:01:03Z |
| institution | BVB |
| isbn | 082183228X |
| language | English |
| lccn | 2003052359 |
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| physical | VII, 197 S. graph. Darst. |
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| series2 | SMF/AMS texts and monographs Panoramas et synthèses |
| spelling | Dynamique et géométrie complexes Complex dynamics and geometry Dominique Cerveau ... Providence, RI American Math. Soc. 2003 VII, 197 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier SMF/AMS texts and monographs 10 Panoramas et synthèses 8 Globale Analysis (DE-588)4021285-3 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Singularität Mathematik (DE-588)4077459-4 gnd rswk-swf Globale Analysis (DE-588)4021285-3 s Dynamisches System (DE-588)4013396-5 s Singularität Mathematik (DE-588)4077459-4 s 1\p DE-604 Cerveau, Dominique ctb SMF/AMS texts and monographs 10 (DE-604)BV013184477 10 Panoramas et synthèses 8 (DE-604)BV037491878 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018481670&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Complex dynamics and geometry SMF/AMS texts and monographs Panoramas et synthèses Globale Analysis (DE-588)4021285-3 gnd Dynamisches System (DE-588)4013396-5 gnd Singularität Mathematik (DE-588)4077459-4 gnd |
| subject_GND | (DE-588)4021285-3 (DE-588)4013396-5 (DE-588)4077459-4 |
| title | Complex dynamics and geometry |
| title_alt | Dynamique et géométrie complexes |
| title_auth | Complex dynamics and geometry |
| title_exact_search | Complex dynamics and geometry |
| title_full | Complex dynamics and geometry Dominique Cerveau ... |
| title_fullStr | Complex dynamics and geometry Dominique Cerveau ... |
| title_full_unstemmed | Complex dynamics and geometry Dominique Cerveau ... |
| title_short | Complex dynamics and geometry |
| title_sort | complex dynamics and geometry |
| topic | Globale Analysis (DE-588)4021285-3 gnd Dynamisches System (DE-588)4013396-5 gnd Singularität Mathematik (DE-588)4077459-4 gnd |
| topic_facet | Globale Analysis Dynamisches System Singularität Mathematik |
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