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math.DS2006
Virtual Immediate Basins of Newton Maps and Asymptotic Values
Xavier Buff, Johannes Rueckert
Newton's root finding method applied to a (transcendental) entire function f:C->C is the iteration of a meromorphic function N. It is well known that if for some starting value z,…
math.DS2005
On Newton's Method for Entire Functions
Johannes Rueckert, Dierk Schleicher
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 be…