Jacobian pairs for planar analytic quadratic-like submersion functions
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.
Authors
- Luis Fernando Mello (ORCID: https://orcid.org/0000-0002-4989-3052)
- Jaume Llibre (ORCID: https://orcid.org/0000-0002-9511-5999)
- Francisco Braun (ORCID: https://orcid.org/0000-0003-3594-9809)
- Matheus Natanael Cassiano
Institutions
- Universitat Autònoma de Barcelona (ES)
- Universidade Federal de São Carlos (BR)
- Reial Acadèmia de Ciències i Arts de Barcelona (ES)
- Universidade Federal de Itajubá (BR)
Publication Details
- Journal
- Journal of Differential Equations
- Published
- 2026-09-11
- DOI
- https://doi.org/10.1016/j.jde.2026.114772
- Primary Topic
- Advanced Differential Equations and Dynamical Systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
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