Sobre la inyectividad en espacios euclidianos

Abstract

We describe some classical results on global injectivity of local dieomorphism on Euclidian spaces. This is not exhaustive, and it does not purport to be a complete history, it simply describes some useful results in injectivity. The first part describes some results related to the Qualitative Theory of Diferential Equations, and presents a characterization of global injectivity on planar applications by using the existence of an isochronous global center. The Global Asymptotic Stability Problem is also described. The second part describes the so called Palais-Smale condition.