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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2019

A combinatorial classification of postcritically fixed Newton maps

Kostiantyn Drach
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Yauhen Mikulich
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Johannes Rückert
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Résumé

We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials as dynamical systems. This lays the foundation for classification results of more general classes of Newton maps. A fundamental ingredient is the proof that for every Newton map (postcritically finite or not) every connected component of the basin of an attracting fixed point can be connected to $\infty$ through a finite chain of such components.

Dates et versions

hal-03285923 , version 1 (13-07-2021)

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Kostiantyn Drach, Yauhen Mikulich, Johannes Rückert, Dierk Schleicher. A combinatorial classification of postcritically fixed Newton maps. Ergodic Theory and Dynamical Systems, 2019, 39 (11), pp.2983-3014. ⟨10.1017/etds.2018.2⟩. ⟨hal-03285923⟩
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