Conjugacies of the Newton maps of rational functions

Roger Barnard; Jeremiah Dwyer; Erin Williams; George Williams

doi:10.1080/17476933.2018.1547285

Conjugacies of the Newton maps of rational functions

Roger Barnard, Jeremiah Dwyer, Erin Williams, George Williams

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4 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 language	English
Pages (from-to)	1666-1685
Number of pages	20
Journal	Complex Variables and Elliptic Equations
Volume	64
Issue number	10
DOIs	https://doi.org/10.1080/17476933.2018.1547285
State	Published - Oct 3 2019

Keywords

37F10
Complex dynamics
Newton map
rational functions
Yuri Antipov

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10.1080/17476933.2018.1547285

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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.",

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AU - Williams, George

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AB - 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.

KW - 37F10

KW - Complex dynamics

KW - Newton map

KW - rational functions

KW - Yuri Antipov

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Conjugacies of the Newton maps of rational functions

Abstract

Keywords

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