Ergodic Theory and Dynamical Systems

Research Article

Multiple attractors in Newton's method

Mike Hurleya1

a1 Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, Ohio 44106, USA

Abstract

For each d ≥ 2 there exists a polynomial p with real coefficients such that the associated Newton function z–[p(z)/p′(z)] has 2d–2 distinct attracting periodic orbits in the complex plane. According to a theorem of G. Julia, this is the maximal number of attracting orbits that any rational function of degree d can possess.

(Received May 29 1985)