Baker domains for Newton's method

Abstract

We show that there exists an entire function without finite asymptotic values for which the associated Newton function tends to infinity in some invariant domain. The question whether such a function exists had been raised by Douady.

8 pages

Cited by in corpus (7)

• On the connectivity of the Julia sets of meromorphic functions
• Absorbing sets and Baker domains for holomorphic maps
• Some examples of Baker domains
• Escaping points in the boundaries of Baker domains
• Newton's method and Baker domains
• An entire function with no fixed points and no invariant Baker domains
• Virtual Immediate Basins of Newton Maps and Asymptotic Values