An extension of the poincaré compactification and a geometric interpretation
DOI:
https://doi.org/10.4067/S0716-09172003000300001Keywords:
Poincaré compactification, Rational vector field, Equilibrium solutions.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.
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