Polynomial maps with nilpotent Jacobians in dimension three

In this paper, we first classify all polynomial maps of the form H=(u(x,y),v(x,y,z),h(x,y,v(x,y,z)))H=(u(x,y),v(x,y,z),h(x,y,v(x,y,z))) in certain conditions. Then we classify some polynomial maps of the form H=(u(x,y),v(x,y,z),h(x,y,z))H=(u(x,y),v(x,y,z),h(x,y,z)).