Foliations, solvability and global injectivity

Francisco Braun, José Ruidival dos Santos Filho, Marco Antonio Teixeira

Let $F:{\mathbb{R}}^n\to {\mathbb{R}}^n$ be a $C^{\infty }$ map such that $DF(x)$ is invertible for every $x\in {\mathbb{R}}^n$. Although being a local diffeomorphism, $F$ is not necessari…