A note on invertible quadratic transformations of the real plane

2015/07/03 by Руслан Шарипов, Sharipov, Ruslan · 1 citation
Engineering · Mathematics · #51M15 #54H15 #57S25 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1507.01861

openalex publication_date 2015/07/03 · openalex created_date 2025/10/10 · 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 quadratic if the degrees of its polynomials are not greater than two. In the present paper an exhaustive description of invertible quadratic transformations of the real plane is given. Their application to the perfect cuboid problem is discussed.

Citations

• Reverse asymptotic estimates for roots of the cuboid characteristic\n equation in the case of the second cuboid conjecture
• Asymptotic estimates for roots of the cuboid characteristic equation in\n the linear region
• A note on rational and elliptic curves associated with the cuboid factor\n equations
• On two elliptic curves associated with perfect cuboids
• On two algebraic parametrizations for rational solutions of the cuboid equations
• On an ideal of multisymmetric polynomials associated with perfect cuboids
• A note on solutions of the cuboid factor equations
• A note on the second cuboid conjecture. Part I
• A note on pairs of metrics in a three-dimensional linear vector space
• On singularities of the inverse problems associated with perfect cuboids
• A strategy of numeric search for perfect cuboids in the case of the second cuboid conjecture
• A general rational solution of an equation associated with perfect cuboids
• The surface parametrizing cuboids
• A counterexamle to the strong real Jacobian conjecture

Cited by

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

Related

• A rough classification of potentially invertible cubic transformations\n of the real plane
• On quartic forms associated with cubic transformations of the real plane
• On quadratic polynomial mappings from the plane into the n dimensional\n space
• On polynomial mappings from the plane to the plane
• On quadratic polynomial mappings f: \Bbb C² → \Bbb C²