Work

Jacobian pairs for planar analytic quadratic-like submersion functions

Year: 2026

Type: article

Abstract: A Jacobian pair for a submersion function f : R 2 → R is a function g : R 2 → R such that the Jacobian determinant of the map ( f , g ) never vanishes. A function f : R 2 → R is called quadratic-like if it is a polynomial of degree 2 in one of the variables. In this note we investigate the existence of Jacobian pairs for analytic quadratic-like submersions.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2026.114772

Authors: Francisco Braun, Matheus Natanael Cassiano, Jaume Llibre, Luis Fernando Mello

Institutions: Universidade Federal de São Carlos, Universitat Autònoma de Barcelona, Reial Acadèmia de Ciències i Arts de Barcelona, Universidade Federal de Itajubá

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Amparo à Pesquisa do Estado de Minas Gerais, Agencia Estatal de Investigación