Displaying similar documents to “Desingularization of three-dimensional vector fields.”

Final forms for a three-dimensional vector field under blowing-up

Felipe Cano (1987)

Annales de l'institut Fourier

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We study the final situations which may be obtained for a singular vector field by permissible blowing-ups of the ambient space (in dimension three). These situations are preserved by permissible blowing-ups and its structure is simple from the view-point of the integral branches. Technically, we take a logarithmic approach, by marking in each step the exceptional divisor of the transformation.

Singularities with exact Poincaré complex but not quasihomogeneous.

Gerhard Pfister, Hans Schönemann (1989)

Revista Matemática de la Universidad Complutense de Madrid

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We give examples of complete intersections in C3 with exact Poincaré complex but not quasihomogeneous using the classification of C.T.C. and the algorithm of Mora.

Instability of equilibria in dimension three

Marco Brunella (1998)

Annales de l'institut Fourier

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In this paper we show that if v is an analytic vector field on ℝ 3 having an isolated singular point at 0, then there exists a trajectory of v which converges to 0 in the past or in the future. The proof is based on certain results concerning desingularizaton of vector fields in dimension three and on index-type arguments .