On quartic forms associated with 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. It turns out that cubic transformations are associated with some binary and quaternary quartic forms. In the present paper these forms are defined and studied.

AmSTeX, 10 pages, amsppt style

References in corpus (4)

• 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

Cited by in corpus (1)

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