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IMI/Publicaţii/BASM/Ediţii/BASM n.1 (44), 2004/

Generating properties of biparabolic invertible polynomial maps in three variables.

Authors: Yu. Bodnarchuk

Abstract

Invertible polynomial map of the standard 1-parabolic form xi -> fi(x1, ...,xn-1), i < n, x n -> alpha*xn + hn(x1, ...,xn-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 TGA3 is generated by an affine group AGL3 and any nonlinear biparabolic map of the form U0*q1*U1*q2*U2, where Ui are linear maps and both qi have the standard 1-parabolic form.

University "Kiev Mohyla Academy"
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Kyiv 40070, Ukraine
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