Conjugacies of the Newton maps of rational functions

Roger W. Barnard, Jerry Dwyer, Erin Williams, G. Brock Williams

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

Newton's method is a well-known iterative method to find roots of a function. The dynamics of the Newton maps of polynomials has long been an object of study, but far less is known about the Newton maps of rational functions. We determine which Newton maps of rational functions are conjugate to quadratic polynomials. We also prove that there are no Newton maps of rational functions which are conjugate to z3.

Original languageEnglish
Pages (from-to)1666-1685
Number of pages20
JournalComplex Variables and Elliptic Equations
Volume64
Issue number10
DOIs
StatePublished - Oct 3 2019

Keywords

  • 37F10
  • Complex dynamics
  • Newton map
  • Yuri Antipov
  • rational functions

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