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Proyecciones (Antofagasta)

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VIDAL, CLAUDIO  and  GOMEZ, PEDRO. AN EXTENSION OF THE POINCARÉ COMPACTIFICATION AND A GEOMETRIC INTERPRETATION. Proyecciones (Antofagasta) [online]. 2003, vol.22, n.3, pp.161-180. ISSN 0716-0917.

Our purpose in this paper is to understand the geometry of the Poincaré compactifcation and to apply this technique to prove that there exists a Poincaré compactifcation of vector felds defned by rational functions and of vector feld that are the quotient of some power of polynomial. We will give also a global expressions for the Poincaré vector feld associated. Furthermore, we summarize these results proving that there exist a Poincaré vector feld for any vector feld whose rate of growth at infnity of each component is not bigger than a polynomial growth.

Keywords : Poincaré compactifcation; rational vector feld; equilibrium solutions.

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