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Poincaré-Hopf index and partial hyperbolicity
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 1, pp. 193-206.

We use the theory of partially hyperbolic systems [HPS] in order to find singularities of index 1 for vector fields with isolated zeroes in a 3-ball. Indeed, we prove that such zeroes exists provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball.

Nous utilisons des systèmes partiellement hyperboliques [HPS] pour trouver des singularités d’indice 1 pour les champs de vecteurs avec singularités isolées sur la boule tridimensionelle. En fait, on trouvera de telles singularités lorsque l’ensemble maximal invariant dans la boule est partiellement hyperbolique, à sous-fibré central volume-dilatant, et les variétés stables fortes sur les singularités sont toutes non nouées.

DOI: 10.5802/afst.1180
C. A Morales 1

1 Instituto de Matematica, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil.
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     title = {Poincar\'e-Hopf index and partial hyperbolicity},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {193--206},
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C. A Morales. Poincaré-Hopf index and partial hyperbolicity. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 1, pp. 193-206. doi : 10.5802/afst.1180. https://afst.centre-mersenne.org/articles/10.5802/afst.1180/

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