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

2007-01-05

arxiv.org/abs/math/0701176v1

Mathematics

Dynamical Systems

21 pages, 3 figures. Submitted to Annales Academiae Scientiarum Fennicae Mathematica

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 infinity through a finite chain of such components.

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