Newton maps for quintic polynomials

@misc{citeulike:86785, 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\$.}, author = {Balibrea, Francisco and Freitas, Orlando and Ramos, Jose S. }, citeulike-article-id = {86785}, eprint = {math.DS/0501327}, keywords = {newton-method, quintic}, month = {January}, posted-at = {2005-02-01 17:18:30}, priority = {2}, title = {Newton maps for quintic polynomials}, url = {http://arxiv.org/abs/math.DS/0501327}, year = {2005} }

TY - ELEC ID - citeulike:86785 L3 - citeulike-article-id:86785 TI - Newton maps for quintic polynomials N2 - 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 $c$. KW - newton-method KW - quintic AU - Balibrea, Francisco AU - Freitas, Orlando AU - Ramos, Jose PY - 2005/01/20/ UR - http://arxiv.org/abs/math.DS/0501327 ER -