VECTOR FIELDS IN R2 WITH MAXIMAL INDEX |
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| Authors: | Nabarro A C; Ruas M A S |
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| Institution: | Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Caixa Postal 668, 13560-970 São Carlos, SP, Brazil |
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| Abstract: | We consider the method of Poincaré to investigate thelocal index of vector fields in the plane. If m is the degreeof the first non-zero jet, Xm, of the vector field X at an isolatedzero, we explore the geometry of the pencil generated by thecoordinate functions of Xm when the absolute value of the indexof X, |ind (X)|, is m. We also find necessary and sufficientconditions for |ind (X)| to be m. |
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