Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2008
|
| Series: | Memoirs of the American Mathematical Society
891 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 191, number 891 (first of five numbers.) |
| Physical Description: | V, 146 S. Ill., graph. Darst. |
| ISBN: | 9780821840566 |
Staff View
MARC
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| 100 | 1 | |a Hubbard, John H. |d 1946- |e Verfasser |0 (DE-588)113172346 |4 aut | |
| 245 | 1 | 0 | |a Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system |c John H. Hubbard ; Peter Papadopol |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2008 | |
| 300 | |a V, 146 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 891 | |
| 500 | |a Volume 191, number 891 (first of five numbers.) | ||
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Equations, Quadratic | |
| 650 | 4 | |a Newton-Raphson method | |
| 650 | 0 | 7 | |a Quadratische Gleichung |0 (DE-588)4198918-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differenzierbares dynamisches System |0 (DE-588)4137931-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Newton-Verfahren |0 (DE-588)4171693-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Newton-Verfahren |0 (DE-588)4171693-0 |D s |
| 689 | 0 | 1 | |a Quadratische Gleichung |0 (DE-588)4198918-1 |D s |
| 689 | 0 | 2 | |a Differenzierbares dynamisches System |0 (DE-588)4137931-7 |D s |
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| 700 | 1 | |a Papadopol, Peter |d 1931- |e Verfasser |0 (DE-588)173995209 |4 aut | |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v 891 |w (DE-604)BV008000141 |9 891 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016328277 | ||
Record in the Search Index
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| adam_text | Table of Contents
Chapter 0 Introduction 1
1. Introduction 1
2. Outline of paper 2
3. Acknowledgements 4
4. A computer tour of Newton s method 4
5. Some open questions 9
Chapter 1 Fundamental properties of Newton maps 11
1.1. Generalities about Newton s method 11
1.2. The intersection of graphs 13
1.3. The Russakovskii-Shiffman measure 18
1.4. Invariant currents 22
1.5. The intersection of conies 23
1.6. Degenerate cases 29
1.7. The one-variable rational functions associated to the roots 32
Chapter 2 Invariant 3-manifolds associated to invariant circles 35
2.1. The circles in the invariant lines 35
2.2. Periodic cycles on invariant circles 38
2.3. Unstable manifolds at infinity 42
2.4. The invariant manifolds of circles 46
2.5. The extension of $ and the origin of bubbles 54
Chapter 3 The behavior at infinity when a = b = 0. 61
3.1. The primitive space 61
3.2. Newton s method and the primitive space 63
Chapter 4 The Farey blow-up 68
4.1. Definition of the Farey blow-up 68
4.2. Naturality of the Farey blow-up 71
4.3. The real oriented blow-up of the Farey blow-up 72
4.4. Naturality and real oriented blow-ups 76
4.5. Inner products on spaces of homogeneous functions 77
4.6. Homology of the Farey blow-up 82
4.7. The action of mappings F/. on homology 86
Chapter 5 The compactification when a = 6 = 0 91
5.1. The tower of blow-ups when a = b = 0 91
5.2. Sequence spaces 95
5.3. The real oriented blow-up of Xqo 97
5.4. The homology of Xx 100
5.5. The action of NP on homology and cohornology 104
5.6. The (co)homology H2(X^,) 114
5.7. The action of N on homology 118
iii
iv Contents
Chapter 6 The case where o and b are arbitrary 123
6.1. A curve of order two 123
6.2. The primitive space for arbitrary a and b 125
6.3. Building the space X^ 126
6.4. The basins of the roots 126
6.5. Real oriented blow-ups and homology 127
Bibliography 128
|
| adam_txt |
Table of Contents
Chapter 0 Introduction 1
1. Introduction 1
2. Outline of paper 2
3. Acknowledgements 4
4. A computer tour of Newton's method 4
5. Some open questions 9
Chapter 1 Fundamental properties of Newton maps 11
1.1. Generalities about Newton's method 11
1.2. The intersection of graphs 13
1.3. The Russakovskii-Shiffman measure 18
1.4. Invariant currents 22
1.5. The intersection of conies 23
1.6. Degenerate cases 29
1.7. The one-variable rational functions associated to the roots 32
Chapter 2 Invariant 3-manifolds associated to invariant circles 35
2.1. The circles in the invariant lines 35
2.2. Periodic cycles on invariant circles 38
2.3. Unstable manifolds at infinity 42
2.4. The invariant manifolds of circles 46
2.5. The extension of $ and the origin of "bubbles" 54
Chapter 3 The behavior at infinity when a = b = 0. 61
3.1. The primitive space 61
3.2. Newton's method and the primitive space 63
Chapter 4 The Farey blow-up 68
4.1. Definition of the Farey blow-up 68
4.2. Naturality of the Farey blow-up 71
4.3. The real oriented blow-up of the Farey blow-up 72
4.4. Naturality and real oriented blow-ups 76
4.5. Inner products on spaces of homogeneous functions 77
4.6. Homology of the Farey blow-up 82
4.7. The action of mappings F/.\ on homology 86
Chapter 5 The compactification when a = 6 = 0 91
5.1. The tower of blow-ups when a = b = 0 91
5.2. Sequence spaces 95
5.3. The real oriented blow-up of Xqo 97
5.4. The homology of Xx 100
5.5. The action of NP on homology and cohornology 104
5.6. The (co)homology H2(X^,) 114
5.7. The action of N on homology 118
iii
iv Contents
Chapter 6 The case where o and b are arbitrary 123
6.1. A curve of order two 123
6.2. The primitive space for arbitrary a and b 125
6.3. Building the space X^ 126
6.4. The basins of the roots 126
6.5. Real oriented blow-ups and homology 127
Bibliography 128 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV023125865 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:53:24Z |
| indexdate | 2024-07-09T21:11:38Z |
| institution | BVB |
| isbn | 9780821840566 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016328277 |
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| physical | V, 146 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | American Math. Soc. |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Hubbard, John H. 1946- Verfasser (DE-588)113172346 aut Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system John H. Hubbard ; Peter Papadopol Providence, RI American Math. Soc. 2008 V, 146 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 891 Volume 191, number 891 (first of five numbers.) Differentiable dynamical systems Equations, Quadratic Newton-Raphson method Quadratische Gleichung (DE-588)4198918-1 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Newton-Verfahren (DE-588)4171693-0 gnd rswk-swf Newton-Verfahren (DE-588)4171693-0 s Quadratische Gleichung (DE-588)4198918-1 s Differenzierbares dynamisches System (DE-588)4137931-7 s DE-604 Papadopol, Peter 1931- Verfasser (DE-588)173995209 aut Memoirs of the American Mathematical Society 891 (DE-604)BV008000141 891 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016328277&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hubbard, John H. 1946- Papadopol, Peter 1931- Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system Memoirs of the American Mathematical Society Differentiable dynamical systems Equations, Quadratic Newton-Raphson method Quadratische Gleichung (DE-588)4198918-1 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Newton-Verfahren (DE-588)4171693-0 gnd |
| subject_GND | (DE-588)4198918-1 (DE-588)4137931-7 (DE-588)4171693-0 |
| title | Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system |
| title_auth | Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system |
| title_exact_search | Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system |
| title_exact_search_txtP | Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system |
| title_full | Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system John H. Hubbard ; Peter Papadopol |
| title_fullStr | Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system John H. Hubbard ; Peter Papadopol |
| title_full_unstemmed | Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system John H. Hubbard ; Peter Papadopol |
| title_short | Newton's method applied to two quadratic equations in C2 viewed as a global dynamical system |
| title_sort | newton s method applied to two quadratic equations in c2 viewed as a global dynamical system |
| topic | Differentiable dynamical systems Equations, Quadratic Newton-Raphson method Quadratische Gleichung (DE-588)4198918-1 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd Newton-Verfahren (DE-588)4171693-0 gnd |
| topic_facet | Differentiable dynamical systems Equations, Quadratic Newton-Raphson method Quadratische Gleichung Differenzierbares dynamisches System Newton-Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016328277&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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