On simple Shamsuddin derivations in two variables

Abstract

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.

Keywords

• dynamical degree
• isotropy group
• Shamsuddin derivations
• simple derivations