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On Newton's method for entire functions
Author(s) -
Rückert Johannes,
Schleicher Dierk
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm046
Subject(s) - library science , citation , subject (documents) , computer science , information retrieval , mathematics
The Newton map N f of an entire function f turns the roots of f into attracting fixed points. Let U be the immediate attracting basin for such a fixed point of N f . We study the behavior of N f in a component V of ℂ\ U . If V can be surrounded by an invariant curve within U and satisfies the condition that for all z ∈ ℂ̂, N f −1 ({ z }) ∩ V is a finite set, then it is shown that V contains another immediate basin of N f or a virtual immediate basin.