Newton's Method Applied to Two Quadratic Equations in C2 Viewed as a Global Dynamical System
Published in February 2008
Book
Paperback/Softback
146 pages
978-0-8218-4056-6 (ISBN)
Description
The authors study the Newton map $N:\mathbb{C 2\rightarrow\mathbb{C 2$ associated to two equations in two unknowns, as a dynamical system. They focus on the first non-trivial case: two simultaneous quadratics, to intersect two conics. In the first two chapters, the authors prove among other things:
More details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Illustrations
illustrations
ISBN-13
978-0-8218-4056-6 (9780821840566)
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Schweitzer Classification
Content
Introduction Fundamental properties of Newton maps Invariant 3-manifolds associated to invariant circles The behavior at infinity when $a=b=0$ The Farey blow-up The compactification when $a=b=0$ The case where $a$ and $b$ are arbitrary Bibliography.