Newton maps for quintic polynomials

Francisco Balibrea; Orlando Freitas; Jose Sousa Ramos

Newton maps for quintic polynomials

Dynamical Systems 2007-05-23 v1 Numerical Analysis

Authors: Francisco Balibrea , Orlando Freitas , Jose Sousa Ramos

Abstract

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 $c$ .

Keywords

thurston maps graph polynomials mapping theory

Cite

@article{arxiv.math/0501327,
  title  = {Newton maps for quintic polynomials},
  author = {Francisco Balibrea and Orlando Freitas and Jose Sousa Ramos},
  journal= {arXiv preprint arXiv:math/0501327},
  year   = {2007}
}

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17 pages, 11 figures

Newton maps for quintic polynomials

Abstract

Keywords

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