AN EXTENSION OF THE POINCARÉ COMPACTIFICATION AND A GEOMETRIC INTERPRETATION

VIDAL, CLAUDIO; GÓMEZ, PEDRO

doi:10.4067/S0716-09172003000300001

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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.22 n.3 Antofagasta dic. 2003

http://dx.doi.org/10.4067/S0716-09172003000300001

Proyecciones
Vol. 22, N o 3, pp. 161-180, December 2003.
Universidad Católica del Norte
Antofagasta - Chile

AN EXTENSION OF THE POINCARÉ
COMPACTIFICATION AND A GEOMETRIC
INTERPRETATION

CLAUDIO VIDAL
Universidade Federal de Pernambuco - Brasil.
PEDRO GÓMEZ
Universidad Federal de Paraiba - Brasil

Abstract

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.

Mathematics Subject Classifcation : 34A34, 34C05, 34A99.

Key Words : Poincaré compactifcation, rational vector feld,
equilibrium solutions.

References

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Received : November 2002.

Claudio Vidal
Departamento de Matemática
Universidade Federal de Pernambuco
Av. Prof. Luiz Freire, s/n
Cidade Universitária
Recife-PE
Brasil
e-mail : claudio@dmat.ufpe.br

and

Pedro Gómez
Departamento de Matemática
Universidade Federal da Paraiba
Cidade Universitária, Jo~ao Pessoa-PB
Brazil
e-mail : venegas@mat.ufpb.br