Newton's method and Baker domains

Abstract

We show that there exists an entire function f without zeros for which the associated Newton function N(z)=z-f(z)/f'(z) is a transcendental meromorphic functions without Baker domains. We also show that there exists an entire function f with exactly one zero for which the complement of the immediate attracting basin has at least two components and contains no invariant Baker domains of N. The second result answers a question of J. Rueckert and D. Schleicher while the first one gives a partial answer to a question of X. Buff.

6 pages

References in corpus (3)

• Iteration of meromorphic functions
• On Newton's Method for Entire Functions
• Baker domains for Newton's method

Cited by in corpus (3)

• On the connectivity of the Julia sets of meromorphic functions
• Absorbing sets and Baker domains for holomorphic maps
• An entire function with no fixed points and no invariant Baker domains