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Resumen de Vector fields in R2 with maximal index

A. C. Nabarro, Maria Aparecida Soares Ruas Árbol académico

  • We consider the method of Poincaré to investigate the local index of vector fields in the plane. If m is the degree of the first non-zero jet, Xm, of the vector field X at an isolated zero, we explore the geometry of the pencil generated by the coordinate functions of Xm when the absolute value of the index of X, |ind (X)|, is m. We also find necessary and sufficient conditions for |ind (X)| to be m.

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