Polynomial maps with nilpotent Jacobians in dimension three II

Abstract

In the paper, we first classify all polynomial maps of the form $H=(u(x,y),v(x,y,z),h(x,y))$ in the case that $JH$ is nilpotent and $({°}_{y}u,{°}_{y}h)\le 3$, $H(0)=0$. Then we classify all polynomial maps of the form $H=(u(x,y,z),v(x,y,u),h(x,y))$ in the case that $JH$ is nilpotent and $(°v(x,y,0),°h)\le 3$, $H(0)=0$. Finally, we classify polynomial maps of the form $H=(u(x,y,z),v(x,y,z),h(x,y))$ in certain conditions.

28 pages