Holdings: Holomorphic dynamics on hyperbolic Riemann surfaces

Holomorphic dynamics on hyperbolic Riemann surfaces:

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Bibliographic Details
Main Author:	Abate, Marco 1962- (Author)
Format:	Book
Language:	English
Published:	Berlin ; Boston De Gruyter [2023]
Series:	De Gruyter Studies in Mathematics Volume 89
Subjects:	Geometrische Funktionentheorie Holomorphe Funktion Komplexe Geometrie Geometrische Funktionentheorie; Holomorphe Funktion; Komplexe Geometrie
Online Access:	https://www.degruyter.com/isbn/9783110601053 Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	XIII, 356 Seiten Illustrationen 24 cm x 17 cm, 755 g
ISBN:	9783110601053 3110601052

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MARC


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653			\|a Geometrische Funktionentheorie
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653			\|a Komplexe Geometrie
653			\|a Geometrische Funktionentheorie; Holomorphe Funktion; Komplexe Geometrie
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adam_text	CONTENTS INTRODUCTION - VII 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 THE SCHWARZ LEMMA AND RIEMANN SURFACES - 1 THE SCHWARZ-PICK LEMMA - 2 THE POINCARE DISTANCE - 8 THE UPPER HALF-PLANE - 14 FIXED POINTS OF AUTOMORPHISMS - 19 MULTIPOINT SCHWARZ-PICK LEMMAS - 28 RIEMANN SURFACES ---- 36 HYPERBOLIC RIEMANN SURFACES AND THE MONTEL THEOREM ---- 54 BOUNDARY BEHAVIOR OF THE UNIVERSAL COVERING MAP - 67 THE POINCARE METRIC - 73 THE AHLFORS LEMMA - 84 BLOCH DOMAINS ---- 88 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 BOUNDARY SCHWARZ LEMMAS - 96 THE JULIA LEMMA - 97 STOLZ REGIONS AND NONTANGENTIAL LIMITS ---- 113 THE JULIA-WOLFF-CARATHEODORY THEOREM - 125 THE LINDELOF THEOREM --- 136 THE WOLFF LEMMA - 143 THE AUTOMORPHISM GROUP OF HYPERBOLIC RIEMANN SURFACES - 147 THE BURNS-KRANTZ THEOREM - 153 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 DISCRETE DYNAMICS ON RIEMANN SURFACES - 158 THE FIXED-POINT CASE ---- 159 THE WOLFF-DENJOY THEOREM - 166 THE HEINS THEOREM - 169 STABILITY OF THE WOLFF POINT ---- 182 MODELS ON RIEMANN SURFACES - 184 RANDOM ITERATION ON BLOCH DOMAINS - 192 RANDOM ITERATION OF SMALL PERTURBATIONS - 201 4 4.1 4.2 4.3 4.4 4.5 4.6 DISCRETE DYNAMICS ON THE UNIT DISK - 212 ELLIPTIC DYNAMICS - 213 SUPERATTRACTING DYNAMICS - 217 HYPERBOLIC DYNAMICS - 221 PARABOLIC DYNAMICS ---- 226 MODELS ON THE UNIT DISK - 234 THE HYPERBOLIC STEP ---- 240 VI - CONTENTS BIBLIOGRAPHY - 337 4.7 4.8 4.9 4.10 PARABOLIC TYPE AND BOUNDARY SMOOTHNESS - 251 BOUNDARY FIXED POINTS - 260 BACKWARD DYNAMICS - 266 COMMUTING FUNCTIONS - 286 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 CONTINUOUS DYNAMICS ON RIEMANN SURFACES - 294 ALGEBRAIC SEMIGROUP HOMOMORPHISMS - 295 ONE-PARAMETER SEMIGROUPS - 297 ONE-PARAMETER SEMIGROUPS ON RIEMANN SURFACES - 300 THE INFINITESIMAL GENERATOR - 304 THE CONTINUOUS WOLFF-DENJOY THEOREM - 313 THE BERKSON-PORTA FORMULA - 315 ONE-PARAMETER SEMIGROUPS ON THE UNIT DISK - 320 A A.1 A. 2 A.3 A.4 A.5 APPENDIX - 325 THE HURWITZ THEOREMS - 325 THE FATOU UNIQUENESS THEOREM - 326 HOLOMORPHIC FUNCTIONS WITH NONNEGATIVE REAL PART - 328 SEQUENCES - 331 TOPOLOGICAL GROUPS - 334 INDEX - 353
adam_txt	CONTENTS INTRODUCTION - VII 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 THE SCHWARZ LEMMA AND RIEMANN SURFACES - 1 THE SCHWARZ-PICK LEMMA - 2 THE POINCARE DISTANCE - 8 THE UPPER HALF-PLANE - 14 FIXED POINTS OF AUTOMORPHISMS - 19 MULTIPOINT SCHWARZ-PICK LEMMAS - 28 RIEMANN SURFACES ---- 36 HYPERBOLIC RIEMANN SURFACES AND THE MONTEL THEOREM ---- 54 BOUNDARY BEHAVIOR OF THE UNIVERSAL COVERING MAP - 67 THE POINCARE METRIC - 73 THE AHLFORS LEMMA - 84 BLOCH DOMAINS ---- 88 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 BOUNDARY SCHWARZ LEMMAS - 96 THE JULIA LEMMA - 97 STOLZ REGIONS AND NONTANGENTIAL LIMITS ---- 113 THE JULIA-WOLFF-CARATHEODORY THEOREM - 125 THE LINDELOF THEOREM --- 136 THE WOLFF LEMMA - 143 THE AUTOMORPHISM GROUP OF HYPERBOLIC RIEMANN SURFACES - 147 THE BURNS-KRANTZ THEOREM - 153 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 DISCRETE DYNAMICS ON RIEMANN SURFACES - 158 THE FIXED-POINT CASE ---- 159 THE WOLFF-DENJOY THEOREM - 166 THE HEINS THEOREM - 169 STABILITY OF THE WOLFF POINT ---- 182 MODELS ON RIEMANN SURFACES - 184 RANDOM ITERATION ON BLOCH DOMAINS - 192 RANDOM ITERATION OF SMALL PERTURBATIONS - 201 4 4.1 4.2 4.3 4.4 4.5 4.6 DISCRETE DYNAMICS ON THE UNIT DISK - 212 ELLIPTIC DYNAMICS - 213 SUPERATTRACTING DYNAMICS - 217 HYPERBOLIC DYNAMICS - 221 PARABOLIC DYNAMICS ---- 226 MODELS ON THE UNIT DISK - 234 THE HYPERBOLIC STEP ---- 240 VI - CONTENTS BIBLIOGRAPHY - 337 4.7 4.8 4.9 4.10 PARABOLIC TYPE AND BOUNDARY SMOOTHNESS - 251 BOUNDARY FIXED POINTS - 260 BACKWARD DYNAMICS - 266 COMMUTING FUNCTIONS - 286 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 CONTINUOUS DYNAMICS ON RIEMANN SURFACES - 294 ALGEBRAIC SEMIGROUP HOMOMORPHISMS - 295 ONE-PARAMETER SEMIGROUPS - 297 ONE-PARAMETER SEMIGROUPS ON RIEMANN SURFACES - 300 THE INFINITESIMAL GENERATOR - 304 THE CONTINUOUS WOLFF-DENJOY THEOREM - 313 THE BERKSON-PORTA FORMULA - 315 ONE-PARAMETER SEMIGROUPS ON THE UNIT DISK - 320 A A.1 A. 2 A.3 A.4 A.5 APPENDIX - 325 THE HURWITZ THEOREMS - 325 THE FATOU UNIQUENESS THEOREM - 326 HOLOMORPHIC FUNCTIONS WITH NONNEGATIVE REAL PART - 328 SEQUENCES - 331 TOPOLOGICAL GROUPS - 334 INDEX - 353
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isbn	9783110601053 3110601052
language	English
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physical	XIII, 356 Seiten Illustrationen 24 cm x 17 cm, 755 g
publishDate	2023
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publishDateSort	2023
publisher	De Gruyter
record_format	marc
series	De Gruyter Studies in Mathematics
series2	De Gruyter Studies in Mathematics
spelling	Abate, Marco 1962- Verfasser (DE-588)102225118X aut Holomorphic dynamics on hyperbolic Riemann surfaces Marco Abate Berlin ; Boston De Gruyter [2023] XIII, 356 Seiten Illustrationen 24 cm x 17 cm, 755 g txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics Volume 89 Geometrische Funktionentheorie Holomorphe Funktion Komplexe Geometrie Geometrische Funktionentheorie; Holomorphe Funktion; Komplexe Geometrie Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe 978-3-11-060197-8 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-059874-2 De Gruyter Studies in Mathematics Volume 89 (DE-604)BV000005407 89 X:MVB https://www.degruyter.com/isbn/9783110601053 B:DE-101 application/pdf https://d-nb.info/1254134158/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034060003&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20220326 DE-101 https://d-nb.info/provenance/plan#vlb
spellingShingle	Abate, Marco 1962- Holomorphic dynamics on hyperbolic Riemann surfaces De Gruyter Studies in Mathematics
title	Holomorphic dynamics on hyperbolic Riemann surfaces
title_auth	Holomorphic dynamics on hyperbolic Riemann surfaces
title_exact_search	Holomorphic dynamics on hyperbolic Riemann surfaces
title_exact_search_txtP	Holomorphic dynamics on hyperbolic Riemann surfaces
title_full	Holomorphic dynamics on hyperbolic Riemann surfaces Marco Abate
title_fullStr	Holomorphic dynamics on hyperbolic Riemann surfaces Marco Abate
title_full_unstemmed	Holomorphic dynamics on hyperbolic Riemann surfaces Marco Abate
title_short	Holomorphic dynamics on hyperbolic Riemann surfaces
title_sort	holomorphic dynamics on hyperbolic riemann surfaces
url	https://www.degruyter.com/isbn/9783110601053 https://d-nb.info/1254134158/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034060003&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000005407
work_keys_str_mv	AT abatemarco holomorphicdynamicsonhyperbolicriemannsurfaces AT walterdegruytergmbhcokg holomorphicdynamicsonhyperbolicriemannsurfaces

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