  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
$(\deg_yu,\deg_yh)\leq 3$, $H(0)=0$. 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
$(\deg v(x,y,0),\deg h)\leq 3$, $H(0)=0$. Finally, we classify polynomial maps
of the form $H=(u(x,y,z),v(x,y,z), h(x,y))$ in certain conditions.
