Categorization of all Newton maps of rational functions conjugate to quadratic polynomials

Date

2013-08

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Abstract

Newton's method is a well-known iterative method to find roots of a function. It has primarily been studied for polynomials, but more recently transcendental functions have also been studied. However, according to our literature search, nothing has been studied for Newton's method for rational functions. Here we extend the known properties of the degree and fixed points of Newton maps of polynomials to Newton maps of rational functions. We also categorize all Newton maps conjugate to quadratic polynomials and show the complications in extending this to degree three Newton maps.

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Keywords

Complex dynamics, Iteration, Newton's map, Mathematics

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