On simple Shamsuddin derivations in two variables

Abstract

We study the subgroup of $k$-automorphisms of $k[x,y]$ which commute with a simple derivation $d$ of $k[x,y]$. We prove, for instance, that this subgroup is trivial when $d$ is a shamsuddin simple derivation. in the general case of simple derivations, we obtain properties for the elements of this subgroup.

dynamical degree; isotropy group; Shamsuddin derivations; simple derivations