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UNINA9910480644103321 |
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Autore |
Hubbard John H (John Hamal), <1945 or 1946-> |
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Titolo |
Newton's method applied to two quadratic equations in C[superscript 2] viewed as a global dynamical system / / John H. Hubbard, Peter Papadopol |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , [2008] |
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©2008 |
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ISBN |
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Descrizione fisica |
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1 online resource (160 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 891 |
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Disciplina |
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Soggetti |
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Newton-Raphson method |
Equations, Quadratic |
Differentiable dynamical systems |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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""Table of Contents""; ""Chapter 0 Introduction""; ""1. Introduction""; ""2. Outline of paper""; ""3. Acknowledgements""; ""4. A computer tour of Newton's method""; ""5. Some open questions""; ""Chapter 1 Fundamental properties of Newton maps""; ""1.1. Generalities about Newton's method""; ""1.2. The intersection of graphs""; ""1.3. The Russakovskii-Shiffman measure""; ""1.4. Invariant currents""; ""1.5. The intersection of conies""; ""1.6. Degenerate cases""; ""1.7. The one-variable rational functions associated to the roots"" |
""Chapter 2 Invariant 3-manifolds associated to invariant circles""""2.1. The circles in the invariant lines""; ""2.2. Periodic cycles on invariant circles""; ""2.3. Unstable manifolds at infinity""; ""2.4. The invariant manifolds of circles""; ""2.5. The extension of Î? and the origin of ""bubbles""""; ""Chapter 3 The behavior at infinity when a = b = 0""; ""3.1. The primitive space""; ""3.2. Newton's method and the primitive space""; ""Chapter 4 The Farey blow-up""; ""4.1. Definition of the Farey blow-up""; ""4.2. Naturality of the Farey blow-up"" |
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