Iteration of rational functions: complex analytic dynamical systems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2000
|
| Ausgabe: | 1. softcover printing |
| Schriftenreihe: | Graduate texts in mathematics
132 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 273 - 277 |
| Beschreibung: | XVI, 280 S. graph. Darst. : 24 cm |
| ISBN: | 0387951512 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | ALAN F. BEARDON ITERATION OF RATIONAL FUNCTIONS COMPLEX ANALYTIC
DYNAMICAL SYSTEMS WITH 35. ILLUSTRATIONS SPRINGER CONTENTS PREFACE VII
PREREQUISITES XV CHAPTER 1 EXAMPLES 1 1.1. INTRODUCTION 1 1.2. ITERATION
OF MOBIUS TRANSFORMATIONS 3 1.3. ITERATION OF Z H-» Z 2 6 1.4.
TCHEBYCHEV POLYNOMIALS 9 1.5. ITERATION OF Z I* Z 2 * 1 13 1.6.
ITERATION OF Z I-+ Z 2 + C 14 1.7. ITERATION OF Z H-F Z + 1/Z 19 1.8.
ITERATION OF Z H-» 2Z - 1/Z 21 1.9. NEWTON S APPROXIMATION 22 1.10.
GENERAL REMARKS 25 CHAPTER 2 RATIONAL MAPS 27 2.1. THE EXTENDED COMPLEX
PLANE 27 2.2. RATIONAL MAPS 30 2.3. THE LIPSCHITZ CONDITION 32 2.4.
CONJUGACY 36 2.5. VALENCY 37 2.6. FIXED POINTS 38 2.7. CRITICAL POINTS
43 2.8. A TOPOLOGY ON THE RATIONAL FUNCTIONS 45 XII CONTENTS CHAPTER 3
THE FATOU AND JULIA SETS 49 3.1. THE FATOU AND JULIA SETS 49 3.2.
COMPLETELY INVARIANT SETS 51 3.3. NORMAL FAMILIES AND EQUICONTINUITY 55
APPENDIX I. THE HYPERBOLIC METRIC 60 CHAPTER 4 PROPERTIES OF THE JULIA
SET 65 4.1. EXCEPTIONAL POINTS 65 4.2. PROPERTIES OF THE JULIA SET 67
4.3. RATIONAL MAPS WITH EMPTY FATOU SET 73 APPENDIX II. ELLIPTIC
FUNCTIONS 77 CHAPTER 5 THE STRUCTURE OF THE FATOU SET 80 5.1. THE
TOPOLOGY OF THE SPHERE 80 5.2. COMPLETELY INVARIANT COMPONENTS OF THE
FATOU SET 82 5.3. THE EULER CHARACTERISTIC 83 5.4. THE RIEMANN-HURWITZ
FORMULA FOR COVERING MAPS 85 5.5. MAPS BETWEEN COMPONENTS OF THE FATOU
SET 90 5.6. THE NUMBER OF COMPONENTS OF THE FATOU SET 93 5.7. COMPONENTS
OF THE JULIA SET 95 CHAPTER 6 PERIODIC POINTS 99 6.1. THE CLASSIFICATION
OF PERIODIC POINTS 99 6.2. THE EXISTENCE OF PERIODIC POINTS 101 6.3.
(SUPER)ATTRACTING CYCLES 104 6.4. REPELLING CYCLES 109 6.5. RATIONALLY
INDIFFERENT CYCLES 110 6.6. IRRATIONALLY INDIFFERENT CYCLES IN F 132
6.7. IRRATIONALLY INDIFFERENT CYCLES IN J 142 6.8. THE PROOF OF THE
EXISTENCE OF PERIODIC POINTS 145 6.9. THE JULIA SET AND PERIODIC POINTS
148 6.10. LOCAL CONJUGACY 150 APPENDIX III. INFINITE PRODUCTS 155
APPENDIX IV. THE UNIVERSAL COVERING SURFACE 157 CHAPTER 7 FORWARD
INVARIANT COMPONENTS 160 7.1. THE FIVE POSSIBILITIES 160 7.2. LIMIT
FUNCTIONS 162 7.3. PARABOLIC DOMAINS 165 7.4. SIEGEL DISCS AND HERMAN
RINGS 167 7.5. CONNECTIVITY OF INVARIANT COMPONENTS 172 CONTENTS XIII
CHAPTER 8 THE NO WANDERING DOMAINS THEOREM 176 8.1. THE NO WANDERING
DOMAINS THEOREM 176 8.2. A PRELIMINARY RESULT 177 8.3. CONFORMAL
STRUCTURES 179 8.4. QUASICONFORMAL CONJUGATES OF RATIONAL MAPS 183 8.5.
BOUNDARY VALUES OF CONJUGATE MAPS 184 8.6. THE PROOF OF THEOREM 8.1.2
186 CHAPTER 9 CRITICAL POINTS 192 9.1. INTRODUCTORY REMARKS 192 9.2. THE
NORMALITY OF INVERSE MAPS 193 9.3. CRITICAL POINTS AND PERIODIC DOMAINS
194 9.4. APPLICATIONS 199 9.5. THE FATOU SET OF A POLYNOMIAL 202 9.6.
THE NUMBER OF NON-REPELLING CYCLES 210 9.7. EXPANDING MAPS 223 9.8.
JULIA SETS AS CANTOR SETS 227 9.9. JULIA SETS AS JORDAN CURVES 232 9.10.
THE MANDELBROT SET 238 CHAPTER 10 HAUSDORFF DIMENSION 246 10.1.
HAUSDORFF DIMENSION 246 10.2. COMPUTING DIMENSIONS 248 10.3. THE
DIMENSION OF JULIA SETS 251 CHAPTER 11 EXAMPLES 257 11.1. SMOOTH JULIA
SETS 257 11.2. DENDRITES 258 11.3. COMPONENTS OF F OF INFINITE
CONNECTIVITY 258 11.4. F WITH INFINITELY CONNECTED AND SIMPLY CONNECTED
COMPONENTS . 260 11.5. J WITH INFINITELY MANY NON-DEGENERATE COMPONENTS
. . . . 261 11.6. F OF INFINITE CONNECTIVITY WITH CRITICAL POINTS IN J
262 11.7. A FINITELY CONNECTED COMPONENT OF F 263 11.8. J IS A CANTOR
SET OF CIRCLES 266 11.9. THE FUNCTION (Z - 2) 2 /Z 2 271 REFERENCES 273
INDEX OF EXAMPLES 278 INDEX 279
|
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| classification_tum | MAT 266f |
| ctrlnum | (OCoLC)51647353 (DE-599)BVBBV013559519 |
| dewey-full | 511.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
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| discipline | Mathematik |
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| indexdate | 2024-07-09T18:47:58Z |
| institution | BVB |
| isbn | 0387951512 |
| language | English |
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| physical | XVI, 280 S. graph. Darst. : 24 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Beardon, Alan F. (DE-588)110704886 aut Iteration of rational functions complex analytic dynamical systems Alan F. Beardon 1. softcover printing New York [u.a.] Springer 2000 XVI, 280 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 132 Literaturverz. S. 273 - 277 Iterative methods (Mathematics) Mappings (Mathematics) Iteration (DE-588)4123457-1 gnd rswk-swf Rationale Funktion (DE-588)4225679-3 gnd rswk-swf Rationale Funktion (DE-588)4225679-3 s Iteration (DE-588)4123457-1 s DE-604 Graduate texts in mathematics 132 (DE-604)BV000000067 132 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009259926&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beardon, Alan F. Iteration of rational functions complex analytic dynamical systems Graduate texts in mathematics Iterative methods (Mathematics) Mappings (Mathematics) Iteration (DE-588)4123457-1 gnd Rationale Funktion (DE-588)4225679-3 gnd |
| subject_GND | (DE-588)4123457-1 (DE-588)4225679-3 |
| title | Iteration of rational functions complex analytic dynamical systems |
| title_auth | Iteration of rational functions complex analytic dynamical systems |
| title_exact_search | Iteration of rational functions complex analytic dynamical systems |
| title_full | Iteration of rational functions complex analytic dynamical systems Alan F. Beardon |
| title_fullStr | Iteration of rational functions complex analytic dynamical systems Alan F. Beardon |
| title_full_unstemmed | Iteration of rational functions complex analytic dynamical systems Alan F. Beardon |
| title_short | Iteration of rational functions |
| title_sort | iteration of rational functions complex analytic dynamical systems |
| title_sub | complex analytic dynamical systems |
| topic | Iterative methods (Mathematics) Mappings (Mathematics) Iteration (DE-588)4123457-1 gnd Rationale Funktion (DE-588)4225679-3 gnd |
| topic_facet | Iterative methods (Mathematics) Mappings (Mathematics) Iteration Rationale Funktion |
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