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

2015/08/19 by Руслан Шарипов, Ruslan Sharipov, Sharipov, Ruslan
Computer Science · Engineering · Mathematics · #14E05 #26B10 #57S25 #Advanced Differential Equations and Dynamical Systems #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #Mathematics, Computing, and Information Processing #Polynomial and algebraic computation #math.AG #msc:14E05 #msc:26B10 #msc:57S25

paper · pdf · doi:10.48550/arxiv.1508.04703

AmSTeX, 8 pages, amsppt style

arxiv created 2015/08/19 · openalex publication_date 2015/08/19 · arxiv updated 2015/08/20 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

A polynomial transformation of the real plane \Bbb R² is a mapping \Bbb R²→\Bbb R² 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 \Bbb R² is suggested. It is based on quartic forms associated with these transformations.

Citations

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

Related

• On quartic forms associated with cubic transformations of the real plane
• A note on invertible quadratic transformations of the real plane
• An Automorphic Classification of Real Cubic Curves
• On the classification of cubic plane Cremona maps
• On Real and Complex Cubic Curves