Article

Acta Applicandae Mathematica

, Volume 13, Issue 1, pp 3-58

Newton's method and complex dynamical systems

  • F. v. HaeselerAffiliated withInstitut für Dynamische Systeme Universität Bremen
  • , H. O. PeitgenAffiliated withInstitut für Dynamische Systeme Universität BremenDepartment of Mathematics UCSC

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Abstract

This article is devoted to the discussion of Newton's method. Beginning with the old results of A.Cayley and E.Schröder we proceed to the theory of complex dynamical systems on the sphere, which was developed by G.Julia and P.Fatou at the beginning of this century, and continued by several mathematicians in recent years.

AMS subject classifications (1980)

30D05 65H05

Key words

Newton method iteration of rational functions Mandelbrot set polynomial-like mappings