Generating properties of biparabolic invertible polynomial maps in three variables

Yu. Bodnarchuk

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2004), pp. 34-39

Résumé

Invertible polynomial map of the standard 1-parabolic form $x_i \to f_i(x_1,\dots,x_{n-1})$, $i$, $x_n\to\alpha x_n+h_n(x_1,\ldots,x_{n-1})$ is a natural generalization of a triangular map. To generalize the previous results about triangular and bitriangular maps, it is shown that the group of tame polynomial transformations $TGA_3$ is generated by an affine group $AGL_3$ and any nonlinear biparabolic map of the form $U_0\cdot q_1\cdot U_1\cdot q_2\cdot U_2,$ where $U_i$ are linear maps and both $q_i$ have the standard 1-parabolic form.