A Combinatorial Classification of Postcritically Fixed Newton Maps

2007/01/05 by Johannes Rückert, Rückert, Johannes · 1 citation
Mathematics · #Mathematical Dynamics and Fractals #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.math/0701176

Abstract

We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials and indicate potential for extensions. As our main tool, we show that for a large class of Newton maps that includes all hyperbolic ones, every component of the basin of an attracting fixed point can be connected to infinity through a finite chain of such components.

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• Gluing polynomials along the circle

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