AN EXTENSION OF THE POINCARÉ COMPACTIFICATION AND A GEOMETRIC INTERPRETATION
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 al...
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| Main Authors: | , |
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| Language: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2003
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| Subjects: | |
| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172003000300001 |
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| Summary: | 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. |
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