An extension of the poincaré compactification and a geometric interpretation
Author
Vidal, Claudio
Gómez, Pedro
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/147910.4067/S0716-09172003000300001
Abstract
Our purpose in this paper is to understand the geometry of the Poincaré compactification and to apply this technique to prove that there exists a Poincaré compactification of vector fields defined by rational functions and of vector field that are the quotient of some power of polynomial. We will give also a global expressions for the Poincaré vector field associated. Furthermore, we summarize these results proving that there exist a Poincaré vector field for any vector field whose rate of growth at infinity of each component is not bigger than a polynomial growth.