Holomorphic dynamics:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English Japanese |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2000
|
| Ausgabe: | Rev. engl. ed., 1. publ. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
66 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 338 S. Ill. |
| ISBN: | 0521662583 9780521662581 |
Internformat
MARC
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| 130 | 0 | |a Fukusō rikigakukei josetsu | |
| 245 | 1 | 0 | |a Holomorphic dynamics |c S. Morosawa ... |
| 250 | |a Rev. engl. ed., 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2000 | |
| 300 | |a XI, 338 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics |v 66 | |
| 650 | 4 | |a Applications holomorphes | |
| 650 | 7 | |a Applications holomorphes |2 ram | |
| 650 | 7 | |a Complexe variabelen |2 gtt | |
| 650 | 7 | |a Differentieerbaarheid |2 gtt | |
| 650 | 4 | |a Dynamique différentiable | |
| 650 | 7 | |a Dynamique différentiable |2 ram | |
| 650 | 7 | |a Dynamische systemen |2 gtt | |
| 650 | 4 | |a Fonctions d'une variable complexe | |
| 650 | 7 | |a Fonctions d'une variable complexe |2 ram | |
| 650 | 7 | |a Holomorfe functies |2 gtt | |
| 650 | 7 | |a Mécanique - Applications holomorphes |2 Rameau | |
| 650 | 7 | |a Sistemas dinâmicos holomorfos |2 larpcal | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Functions of complex variables | |
| 650 | 4 | |a Holomorphic mappings | |
| 650 | 0 | 7 | |a Differenzierbares dynamisches System |0 (DE-588)4137931-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Holomorphe Abbildung |0 (DE-588)4160471-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Morosawa, Shunsuke |e Sonstige |4 oth | |
| 830 | 0 | |a Cambridge studies in advanced mathematics |v 66 |w (DE-604)BV000003678 |9 66 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009089374 | ||
Datensatz im Suchindex
| _version_ | 1804128102401441792 |
|---|---|
| adam_text | Contents
Preface
page
ix
1
Dynamics of polynomial maps
1
1.1
The set of escaping points for a polynomial
2
1.1.1
Typical examples of polynomials
2
1.1.2
Basic properties of the filled Julia set
7
1.2
Local behavior near a fixed point
12
1.2.1 Schröder
equation for
λ
with
|λ|
< 1 12
1.2.2 Schröder
equation for
λ
with
|λ|
= 1 16
1.3
Quadratic polynomials and the Mandelbrot set
20
1.4
Hausdorff dimension and capacity
27
1.4.1
Hausdorff measure
27
1.4.2
Hyperbolicity
29
1.4.3
Capacity
32
1.5
Polynomial-like mappings
35
2
The Fatou set and the Julia set
41
2.1
Holomorphic endomorphisms of planar domains
42
2.1.1
Hyperbolic domains
42
2.1.2
Normal families
45
2.1.3
The Julia set and the Fatou set
47
2.1.4
The classification theorem
49
2.2
Value distribution theory
54
2.2.1
The first main theorem and the characteristic function
54
2.2.2
The second main theorem and direct consequences
57
2.2.3
More on entire functions
62
2.3
Basic properties of the Julia set
64
2.3.1
Other characterizations of the Julia set
64
2.3.2
The first fundamental theorem
69
2.4 Singular
values
and Fatou
components
73
2.4.1
Singular values and periodic components
73
2.4.2
The
Teichmüller
space of complex dynamics
77
2.4.3
The second fundamental theorem
80
3
Dynamics of entire functions
85
3.1
Basic dynamical properties of entire functions
85
3.1.1
Topological properties of the Fatou set and the Julia set
86
3.1.2
Special classes of entire functions
88
3.1.3
Escaping points
93
3.2
The exponential family
96
3.2.1
The Cantor bouquet
97
3.2.2
The size of the Julia set
100
3.2.3
The representation space
105
3.3
Topological completeness for decorated exponential families
106
3.4
Examples
112
3.4.1
Wandering domains
112
3.4.2
Logarithmic lifts and Baker domains
119
4
Dynamics of rational functions
124
4.1
Topics on the Newton method
124
4.1.1
The Newton method
124
4.1.2
Iterative algorithms and computability over the reals
127
4.2
Fundamental theorems of Fatou, Julia and Sullivan
132
4.3
Theorems of Shishikura
141
4.4
The Julia sets of hyperbolic rational functions
149
5
Kleinian groups and Sullivan s dictionary
163
5.1
The limit sets and the ordinary sets
163
5.2
Sullivan s dictionary
173
5.3
Stability
179
5.4
Conformai
density and Hausdorff dimension
187
6
Dynamics of holomorphic maps of several variables
198
6.1
Preparation from complex analysis of several variables
198
6.2
Local theory at attracting or repelling fixed points
209
6.3
Holomorphic automorphisms of C2 and Fatou-Bieberbach
domains
214
6.4
Behavior at a fixed point of saddle type
220
7
Dynamics of generalized
Hénon
maps
225
7.1
Polynomial automorphisms of C2 of degree
2 225
7.2
Sets of escaping points and non-escaping points
235
7.3
Structure of the set of escaping points
241
7.4
The set of non-escaping points and symbolic dynamics
251
8
Pluripotential theory of polynomial automorphisms
263
8.1
Positive currents
264
8.2
Lelong s theorem
270
8.3
Fundamental properties of polynomial automorphisms
276
8.4
Pluricomplex Green functions
288
8.5
Stable and unstable convergence theorems
295
8.6
Currents for analytic subsets
304
9
Dynamics of polynomial automorphisms
310
9.1
The stable and unstable sets
310
9.2
Applications of the convergence theorems
318
9.3
Hyperbolic polynomial automorphisms
321
Bibliography
329
Index
335
|
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| discipline | Mathematik |
| edition | Rev. engl. ed., 1. publ. |
| format | Book |
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| id | DE-604.BV013330548 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:54Z |
| institution | BVB |
| isbn | 0521662583 9780521662581 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009089374 |
| oclc_num | 40964688 |
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| owner | DE-355 DE-BY-UBR DE-384 DE-739 DE-11 DE-19 DE-BY-UBM DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-739 DE-11 DE-19 DE-BY-UBM DE-20 |
| physical | XI, 338 S. Ill. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Fukusō rikigakukei josetsu Holomorphic dynamics S. Morosawa ... Rev. engl. ed., 1. publ. Cambridge Cambridge Univ. Press 2000 XI, 338 S. Ill. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 66 Applications holomorphes Applications holomorphes ram Complexe variabelen gtt Differentieerbaarheid gtt Dynamique différentiable Dynamique différentiable ram Dynamische systemen gtt Fonctions d'une variable complexe Fonctions d'une variable complexe ram Holomorfe functies gtt Mécanique - Applications holomorphes Rameau Sistemas dinâmicos holomorfos larpcal Differentiable dynamical systems Functions of complex variables Holomorphic mappings Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Holomorphe Abbildung (DE-588)4160471-4 gnd rswk-swf Komplexe Variable (DE-588)4164905-9 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Holomorphe Abbildung (DE-588)4160471-4 s Komplexe Variable (DE-588)4164905-9 s DE-604 Morosawa, Shunsuke Sonstige oth Cambridge studies in advanced mathematics 66 (DE-604)BV000003678 66 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009089374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Holomorphic dynamics Cambridge studies in advanced mathematics Applications holomorphes Applications holomorphes ram Complexe variabelen gtt Differentieerbaarheid gtt Dynamique différentiable Dynamique différentiable ram Dynamische systemen gtt Fonctions d'une variable complexe Fonctions d'une variable complexe ram Holomorfe functies gtt Mécanique - Applications holomorphes Rameau Sistemas dinâmicos holomorfos larpcal Differentiable dynamical systems Functions of complex variables Holomorphic mappings Differenzierbares dynamisches System (DE-588)4137931-7 gnd Holomorphe Abbildung (DE-588)4160471-4 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4160471-4 (DE-588)4164905-9 |
| title | Holomorphic dynamics |
| title_alt | Fukusō rikigakukei josetsu |
| title_auth | Holomorphic dynamics |
| title_exact_search | Holomorphic dynamics |
| title_full | Holomorphic dynamics S. Morosawa ... |
| title_fullStr | Holomorphic dynamics S. Morosawa ... |
| title_full_unstemmed | Holomorphic dynamics S. Morosawa ... |
| title_short | Holomorphic dynamics |
| title_sort | holomorphic dynamics |
| topic | Applications holomorphes Applications holomorphes ram Complexe variabelen gtt Differentieerbaarheid gtt Dynamique différentiable Dynamique différentiable ram Dynamische systemen gtt Fonctions d'une variable complexe Fonctions d'une variable complexe ram Holomorfe functies gtt Mécanique - Applications holomorphes Rameau Sistemas dinâmicos holomorfos larpcal Differentiable dynamical systems Functions of complex variables Holomorphic mappings Differenzierbares dynamisches System (DE-588)4137931-7 gnd Holomorphe Abbildung (DE-588)4160471-4 gnd Komplexe Variable (DE-588)4164905-9 gnd |
| topic_facet | Applications holomorphes Complexe variabelen Differentieerbaarheid Dynamique différentiable Dynamische systemen Fonctions d'une variable complexe Holomorfe functies Mécanique - Applications holomorphes Sistemas dinâmicos holomorfos Differentiable dynamical systems Functions of complex variables Holomorphic mappings Differenzierbares dynamisches System Holomorphe Abbildung Komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009089374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | UT fukusorikigakukeijosetsu AT morosawashunsuke holomorphicdynamics |