Quadratic and cubic Newton maps of rational functions

Tarakanta Nayak; Soumen Pal

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arXiv · 2004.06899

Quadratic and cubic Newton maps of rational functions

Tarakanta Nayak·Soumen Pal

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Abstract

The dynamics of all quadratic Newton maps of rational functions are completely described. The Julia set of such a map is found to be either a Jordan curve or totally disconnected. It is proved that no Newton map with degree at least three of any rational function is conformally conjugate to a unicritical polynomial(i.e., with exactly one finite critical point). However, there are cubic Newton maps which are conformally conjugate to other polynomials. The Julia set of such a Newton map is shown to be a closed curve. It is a Jordan curve whenever the Newton map has two attracting fixed points.

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Tarakanta Nayak, Soumen Pal. 2020-04-15. Quadratic and cubic Newton maps of rational functions. https://arxiv.org/abs/2004.06899

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