Tame and wild automorphisms of differential polynomial algebras of rank 2

Abstract: It is proved that the tame automorphism group of a differential polynomial algebra $k{x,y}$ over a field $k$ of characteristic $0$ in two variables $x,y$ with $m$ commuting derivations $\delta_1, \ldots, \delta_m$ is a free product with amalgamation. An example of a wild automorphism of the algebra $k{x,y}$ in the case of $m\geq 2$ derivations is constructed.