1.

Record Nr.

UNINA9910480644103321

Autore

Hubbard John H (John Hamal), <1945 or 1946->

Titolo

Newton's method applied to two quadratic equations in C[superscript 2] viewed as a global dynamical system / / John H. Hubbard, Peter Papadopol

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , [2008]

©2008

ISBN

1-4704-0497-4

Descrizione fisica

1 online resource (160 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 891

Disciplina

515/.39

Soggetti

Newton-Raphson method

Equations, Quadratic

Differentiable dynamical systems

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

""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""