An extension of the poincaré compactification and a geometric interpretation

• Vidal, Claudio ^[1] ; Gómez, Pedro ^[2]
  1. [1] Universidade Federal de Pernambuco

     Universidade Federal de Pernambuco

     Brasil

     
  2. [2] Universidade Federal da Paraíba

     Universidade Federal da Paraíba

     Brasil

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 22, Nº. 3, 2003, págs. 161-180
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.