The Global Injectivity of $$C^2$$ Maps in $$\mathbb R^2$$
Abstract Let F be a $$C^{2}$$ C 2 map from the real plane into itself whose Jacobian determinant is nonzero at every point. By the Inverse Function Theorem, such a map is locally injective. A classical and challenging problem is to determine conditions under which F is globally injective. In this work, using results from the qualitative theory of differential equations, we provide both a necessary and sufficient condition and a sufficient condition for the global injectivity of F .
Authors
- Luis Fernando Mello (ORCID: https://orcid.org/0000-0002-4989-3052)
- Jaume Llibre (ORCID: https://orcid.org/0000-0002-9511-5999)
Institutions
- Universitat Autònoma de Barcelona (ES)
- Universidade Federal de Itajubá (BR)
Publication Details
- Journal
- Bulletin of the Brazilian Mathematical Society New Series
- Published
- 2026-08-25
- DOI
- https://doi.org/10.1007/s00574-026-00525-3
- 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
- Fundação de Amparo à Pesquisa do Estado de Minas Gerais