Complex dynamical systems and the geometry of domains in Banach spaces:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Warszawa
Polska Akad. Nauk, Inst. Matematyczny
2004
|
| Schriftenreihe: | Dissertationes mathematicae
427 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 62, II S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Complex dynamical systems and the geometry of domains in Banach spaces |c Mark Elin ; Simeon Reich ; David Shoikhet |
| 264 | 1 | |a Warszawa |b Polska Akad. Nauk, Inst. Matematyczny |c 2004 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Complex dynamical systems and the geometry of domains in Banach spaces
Autor: Elin, Mark
Jahr: 2004
CONTENTS
0. Introduction....................................................................................................................................................5
1. Basic concepts and definitions..................................................................................................................7
1.1. Holomorphic mappings........................................................................................................................7
1.2. Convex, star-shaped and spiral-shaped domains......................................................................8
1.3. Fan-like and snail-like mappings......................................................................................................9
2. Historical sketch............................................................................................................................................10
2.1. Star-like functions on the unit disk................................................................................................10
2.3. Spiral-like functions on the unit disk............................................................................................11
2.3. Convex and close-to-convex functions ..........................................................................................11
2.4. Fan-shaped functions. A conjecture of M. S. Robertson........................................................12
2.5. Higher dimensional extensions ........................................................................................................13
3. Dynamical approach....................................................................................................................................17
3.1. Semicomplete vector fields and semigroups of holomorphic mappings..............................17
3.2. Stationary points of semigroups of holomorphic mappings ..................................................18
3.3. Boundary and interior flow invariance conditions....................................................................19
3.4. Bounded symmetric domains and complete vector fields......................................................23
3.5. Characterizations of semicomplete vector fields........................................................................24
3.6. Strongly semicomplete vector fields and rates of convergence of semigroups................27
3.7. Flows and vector fields on biholomorphically equivalent domains and geometric
aspects in Banach spaces....................................................................................................................30
3.8. Parametric representations of semicomplete vector fields on the Hilbert ball................37
3.8.1. The one-dimensional Berkson-Porta formula................................................................37
3.8.2. A characterization of semicomplete vector fields on the Hilbert ball with an
interior null point...........................................................
3.8.3. Comparison of solutions of evolution equations: asymptotic behavior..................40
3.8.4. Admissible lower and upper bounds and rates of convergence................................42
3.8.5. A parametric representation of semicomplete vector fields with an interior
null point......................................................................................................................................^9
3.8.6. A parametric representation of semicomplete vector fields with no null point. 51
3.9. Growth and covering theorems for star-like mappings on the unit ball of Banach
and Hilbert spaces................................................................................................................................^
References...............................................................................
2000 Mathematics Subject Classification: 30C45, 32F45, 34G20, 46G20, 46T25, 47H20.
Key words and phrases: asymptotic behavior, complete and semicomplete vector fields, holomor-
phic generators, growth and covering theorems, nonlinear semigroups, star-like and spiral-like
mappings.
Received 26.3.2003.
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:00:56Z |
| institution | BVB |
| language | English |
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| physical | 62, II S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Polska Akad. Nauk, Inst. Matematyczny |
| record_format | marc |
| series | Dissertationes mathematicae |
| series2 | Dissertationes mathematicae |
| spelling | Elin, Mark Verfasser aut Complex dynamical systems and the geometry of domains in Banach spaces Mark Elin ; Simeon Reich ; David Shoikhet Warszawa Polska Akad. Nauk, Inst. Matematyczny 2004 62, II S. txt rdacontent n rdamedia nc rdacarrier Dissertationes mathematicae 427 Biholomorphic mappings Geometric function theory Holomorphic mappings Holomorphe Abbildung (DE-588)4160471-4 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Holomorphe Abbildung (DE-588)4160471-4 s Banach-Raum (DE-588)4004402-6 s DE-604 Reich, Simeon Verfasser aut Shoiykhet, David 1953- Verfasser (DE-588)1079700099 aut Dissertationes mathematicae 427 (DE-604)BV000003039 427 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012925667&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Elin, Mark Reich, Simeon Shoiykhet, David 1953- Complex dynamical systems and the geometry of domains in Banach spaces Dissertationes mathematicae Biholomorphic mappings Geometric function theory Holomorphic mappings Holomorphe Abbildung (DE-588)4160471-4 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4160471-4 (DE-588)4004402-6 |
| title | Complex dynamical systems and the geometry of domains in Banach spaces |
| title_auth | Complex dynamical systems and the geometry of domains in Banach spaces |
| title_exact_search | Complex dynamical systems and the geometry of domains in Banach spaces |
| title_full | Complex dynamical systems and the geometry of domains in Banach spaces Mark Elin ; Simeon Reich ; David Shoikhet |
| title_fullStr | Complex dynamical systems and the geometry of domains in Banach spaces Mark Elin ; Simeon Reich ; David Shoikhet |
| title_full_unstemmed | Complex dynamical systems and the geometry of domains in Banach spaces Mark Elin ; Simeon Reich ; David Shoikhet |
| title_short | Complex dynamical systems and the geometry of domains in Banach spaces |
| title_sort | complex dynamical systems and the geometry of domains in banach spaces |
| topic | Biholomorphic mappings Geometric function theory Holomorphic mappings Holomorphe Abbildung (DE-588)4160471-4 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Biholomorphic mappings Geometric function theory Holomorphic mappings Holomorphe Abbildung Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012925667&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003039 |
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