Newton maps for quintic polynomials

Details Newton maps for quintic polynomials Newton maps for quintic polynomials

2005-01-20

arxiv.org/abs/math/0501327v1

Mathematics

Dynamical Systems

17 pages, 11 figures

Scientific paper

The purpose of this paper is to study some properties of the Newton maps associated to real quintic polynomials. First using the Tschirnhaus transformation, we reduce the study of Newton's method for general quintic polynomials to the case $f(x)=x^{5}-c x+1$. Then we use symbolic dynamics to consider this last case and construct a kneading sequences tree for Newton maps. Finally, we prove that the topological entropy is a monotonic non-decreasing map with respect to the parameter $c$.

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