A rough classification of potentially invertible cubic transformations of the real plane

Abstract

A polynomial transformation of the real plane R 2 is a mapping R 2 → R 2 given by two polynomials of two variables. Such a transformation is called cubic if the degrees of its polynomials are not greater than three. In the present paper a rough classification scheme for cubic transformations of R 2 is suggested. It is based on quartic forms associated with these transformations.