The classification of some polynomial maps with nilpotent Jacobians

In the paper, we first classify all polynomial maps $H$ of the following form: $H=big(H_1(x_1,x_2,ldots,x_n),H_2(x_1,x_2),H_3(x_1,x_2),ldots,H_n(x_1,x_2)big)$ with $JH$ nilpotent. After that, we generalize the structure of $H$ to $H=big(H_1(x_1,x_2,ldots,x_n),H_2(x_1,x_2),H_3(x_1,x_2,H_1),ldots,H_n(x_1,x_2,H_1)big)$.