Abstract
AbstractThe 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 ∈ ℂ, 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.
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