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A polynomial transformation of the real plane $\Bbb R^2$ is a mapping $\BbbR^2\to\Bbb R^2$ given by two polynomials of two variables. Such atransformation is called cubic if the degrees of its polynomials are notgreater than three. In the present paper a rough classification scheme forcubic transformations of $\Bbb R^2$ is suggested. It is based on quartic formsassociated with these transformations.

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