Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
Linz
Univ.-Verl. Trauner
2000
|
| Schriftenreihe: | Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz / C]
32 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | I, 168 S. Ill., graph. Darst. |
| ISBN: | 3854871384 |
Internformat
MARC
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| 100 | 1 | |a Stroh, Christoph Martin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer |c Christoph Martin Stroh |
| 264 | 1 | |a Linz |b Univ.-Verl. Trauner |c 2000 | |
| 300 | |a I, 168 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz / C] |v 32 | |
| 502 | |a Zugl.: Linz, Univ., Diss., 2000 | ||
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| 650 | 7 | |a Iteration |2 gtt | |
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| 650 | 7 | |a Rationale Funktion |2 gtt | |
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Datensatz im Suchindex
| _version_ | 1804128001099563008 |
|---|---|
| adam_text | Contents
1 Introduction and Basic Material 1
1.1 Introduction 1
1.2 Sets and Proper Mappings 2
1.3 The Julia Set and the Fatou Set 6
1.3.1 Definitions and Basic Properties 6
1.3.2 Attracting Fixed Points 9
1.3.3 Rationally Indifferent Fixed Points 14
1.3.4 Rotation Domains 16
1.3.5 Hyperbolic Mappings 17
1.4 Quasiconformal Mappings 17
1.5 Polynomial like Mappings 19
2 Julia and Mandelbrot Sets of Chebyshev Families 25
2.1 Motivation and Preliminaries 25
2.2 On the Quadratic likeness of Td, 29
2.3 On the Mandelbrot Set MTd 34
2.3.1 The Center Component of Mrt — Quasicircles 34
2.3.2 Small Copies of M in MTd 38
2.4 Bounds for JTd x 41
2.5 Chebyshev like Rational Functions 49
3 Connectedness of Julia Sets 57
3.1 General Results and Completely Invariant Components 58
3.2 About the Connectedness of a Basin of Attraction 62
3.3 Connectedness of the Julia Set Itself 69
3.4 Connectedness under Special Assumptions 74
3.5 Real Rational Functions 78
3.6 On the Connectedness of a Family of Cubic Rational Functions 85
3.7 Exotic Basins 88
3.7.1 Real Critical Points 89
3.7.2 The Proof of Proposition 3.50 93
3.7.3 Complex Critical Points 99
3.7.4 Examples 103
3.8 Asymptotic Behavior of Julia Sets 104
4 Quasicircles 109
4.1 General Results 109
4.2 Schur Polynomials 114
ii Contents
5 The Computer Program 121
5.1 Background 121
5.2 Settings 122
5.2.1 What the Program Does at Startup 122
5.2.2 Parameters the User Can Adjust 123
5.3 The Main Drawing Methods 124
5.3.1 Generating Color Images 124
5.3.2 Drawing the Julia Set Only 126
5.4 Additional Items RatioMia Visualizes 127
5.4.1 Circles, Disks, and Petals 127
5.4.2 Various Sets 128
5.4.3 Points and Orbits 128
5.4.4 Graphs 129
5.5 Modifications of RatioJulia 130
A Constructing Rational Functions 131
B Escape and Converge Radii and Attracting Petals 133
B.I Escape Radii 133
B.2 Converge Radii 137
B.3 Attracting Petals 142
C Visualizing Julia Sets and More on the Computer 149
C.I Standard Methods in the Plane 149
C.I.I Colorizing the Fatou Set 149
C.1.2 Fixed Points with Derivative 1 150
C.2 Visualizing on the Sphere 151
C.2.1 The Subroutine planetosphere 152
C.2.2 The Function spheretoplane 153
C.2.3 The Subroutine screentosphere 153
C.2.4 The Function spheretoscreen 155
C.3 Visualizing Level Lines 157
List of Symbols 159
Index 161
Bibliography 163
|
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| ctrlnum | (OCoLC)47313793 (DE-599)BVBBV013240830 |
| discipline | Mathematik |
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| id | DE-604.BV013240830 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:42:18Z |
| institution | BVB |
| isbn | 3854871384 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009023410 |
| oclc_num | 47313793 |
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| owner_facet | DE-739 DE-355 DE-BY-UBR DE-83 |
| physical | I, 168 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Univ.-Verl. Trauner |
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| series2 | Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz / C] |
| spelling | Stroh, Christoph Martin Verfasser aut Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer Christoph Martin Stroh Linz Univ.-Verl. Trauner 2000 I, 168 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz / C] 32 Zugl.: Linz, Univ., Diss., 2000 Fatou-Menge gtt Iteration gtt Julia-Menge gtt Rationale Funktion gtt Julia-Menge (DE-588)4431306-8 gnd rswk-swf Rationale Funktion (DE-588)4225679-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Julia-Menge (DE-588)4431306-8 s Rationale Funktion (DE-588)4225679-3 s DE-604 C] Universität <Linz>: [Schriften der Johannes-Kepler-Universität Linz 32 (DE-604)BV009806089 32 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009023410&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stroh, Christoph Martin Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer Fatou-Menge gtt Iteration gtt Julia-Menge gtt Rationale Funktion gtt Julia-Menge (DE-588)4431306-8 gnd Rationale Funktion (DE-588)4225679-3 gnd |
| subject_GND | (DE-588)4431306-8 (DE-588)4225679-3 (DE-588)4113937-9 |
| title | Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer |
| title_auth | Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer |
| title_exact_search | Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer |
| title_full | Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer Christoph Martin Stroh |
| title_fullStr | Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer Christoph Martin Stroh |
| title_full_unstemmed | Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer Christoph Martin Stroh |
| title_short | Julia Sets of rational functions with special emphasis on Chebyshev Families, connectedness, and visualization on the computer |
| title_sort | julia sets of rational functions with special emphasis on chebyshev families connectedness and visualization on the computer |
| topic | Fatou-Menge gtt Iteration gtt Julia-Menge gtt Rationale Funktion gtt Julia-Menge (DE-588)4431306-8 gnd Rationale Funktion (DE-588)4225679-3 gnd |
| topic_facet | Fatou-Menge Iteration Julia-Menge Rationale Funktion Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009023410&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009806089 |
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