Abstract:

We discuss some preliminary results and possible future research about dynamical and parameter plane of Newton method applied to the family of $n$-degree polynomials $P_c^n(z)=z^n-cz+1$ with special attention to the case $n=5$. This family (for $n=5$) is obtained by considering a Tschirnhaus transformation of the whole family of quintic polynomials.
This is a work in process with B. Campos, T. Garijo and P. Vindel.