5 problems

Let $D$ be a derivation as in case $c)$ of Theorem, and let ${\rm Aut}(D)$ denote its automorphism group. Finiteness conjecture. In case $c)$ of Theorem, the group ${\rm Aut}(D)$ i…

Kernel conjecture.

Let $D$ be a nonzero derivation of ${\rm K}[x,y]$, where ${\rm K}$ is the underlying field, and let ${\mathbb e}(D)$ denote the eigenvalue-degree invariant used in the paper. Finit…

Finiteness conjecture. If $D$ is simple, then

Kernel-growth conjecture. The dimension $\dim K_m$ grows polynomially in $m$ of degree at most $N-2$.