The classification of some polynomial maps in dimension three

In the paper, we classify all polynomial maps of the form $H=(u(x,y),v(x,y,z),h(x,y,z))$ in the case that $JH$ is nilpotent and ${\mathrm{°}}_{z}v\ge 2{\mathrm{°}}_{z}h$. Then we give the structure of $H=(u(x,y),v(x,y,z),h(x,y,z))$ if $JH$ is nilpotent and ${\mathrm{°}}_{z}h\le 3$.