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


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)