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Multiple attractors in Newton's method

Published online by Cambridge University Press:  19 September 2008

Mike Hurley
Mike Hurley
Affiliation:
Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, Ohio 44106, USA
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Abstract

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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 4 , December 1986 , pp. 561 - 569
Copyright
Copyright © Cambridge University Press 1986

References

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