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Dynamics of Newton maps
Published online by Cambridge University Press: 15 February 2022
Abstract
In this paper, we study the dynamics of the Newton maps for arbitrary polynomials. Let p be an arbitrary polynomial with at least three distinct roots, and f be its Newton map. It is shown that the boundary $\partial B$ of any immediate root basin B of f is locally connected. Moreover, $\partial B$ is a Jordan curve if and only if $\mathrm {deg}(f|_B)=2$ . This implies that the boundaries of all components of root basins, for the Newton maps for all polynomials, from the viewpoint of topology, are tame.
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- © The Author(s), 2022. Published by Cambridge University Press
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