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

Abstract

A polynomial transformation of the real plane ${\mathbb{R}}^2$ is a mapping ${\mathbb{R}}^2\to {\mathbb{R}}^2$ 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 ${\mathbb{R}}^2$ is suggested. It is based on quartic forms associated with these transformations.

AmSTeX, 8 pages, amsppt style

References in corpus (5)

• Course of analytical geometry
• Asymptotic estimates for roots of the cuboid characteristic equation in the linear region
• A note on invertible quadratic transformations of the real plane
• On the Rational Real Jacobian Conjecture
• On quartic forms associated with cubic transformations of the real plane