A Combinatorial classification of postcritically fixed Newton maps

Details A Combinatorial classification of postcritically fixed Newton maps A Combinatorial classification of postcritically fixed Newton maps

2010-10-25

arxiv.org/abs/1010.5280v1

Mathematics

Dynamical Systems

22 pages, 3 figures

Scientific paper

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 $\infty$ through a finite chain of such components.

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