### 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 z^{3}.

Original language | English |
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Pages (from-to) | 1666-1685 |

Number of pages | 20 |

Journal | Complex Variables and Elliptic Equations |

Volume | 64 |

Issue number | 10 |

DOIs | |

State | Published - Oct 3 2019 |

### Keywords

- 37F10
- Complex dynamics
- Newton map
- Yuri Antipov
- rational functions

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## Cite this

Barnard, R. W., Dwyer, J., Williams, E., & Williams, G. B. (2019). Conjugacies of the Newton maps of rational functions.

*Complex Variables and Elliptic Equations*,*64*(10), 1666-1685. https://doi.org/10.1080/17476933.2018.1547285