## Abstract

Newton’s method is a well-known iterative method to find roots of a function. The related Newton maps have primarily been studied for polynomials, but recently extended to rational and transcendental functions. We describe how a rational function r influences the degree and fixed points of its Newton map R. We then analyze the Julia sets of the Newton maps of Möbius transformations. In doing so, we verify a conjecture of Corte and expand on that result. We also consider Newton maps of rational functions of the form (z-r1)(z-r2)z-p. We prove that these Newton maps are all conjugate to z^{2}, allowing us to completely describe their Julia sets.

Original language | English |
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Pages (from-to) | 1055-1070 |

Number of pages | 16 |

Journal | Journal of Analysis |

Volume | 29 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2021 |

## Keywords

- Complex dynamics
- Newton map
- Rational functions