Abstract
The dynamics of all quadratic Newton maps of rational functions is 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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Acknowledgements
The first author acknowledges SERB, Government of India for financial support through a MATRICS project. The second author is supported by the University Grants Commission, Government of India.
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Communicated by Parameswaran Sankaran.
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Nayak, T., Pal, S. Quadratic and cubic Newton maps of rational functions. Proc Math Sci 132, 46 (2022). https://doi.org/10.1007/s12044-022-00688-1
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DOI: https://doi.org/10.1007/s12044-022-00688-1