On Isotropy Group of Danielewski Surfaces

In the present work we consider differential rings of the form $(\mathcal B,D)$ where $\mathcal B$ is a Danielewski surface and $D$ is a locally nilpotent derivation on $\mathcal B$. Influenced by several recent works, we describe the isotropy group of a locally nilpotent derivation, $D$, on Danielewski surfaces, in the cases $xy = φ(z)$, $x^ny=φ(Z)$, and $f(x)x = φ(z)$.

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