Poincaré-Hopf index and partial hyperbolicity
The author uses the theory of partially hyperbolic systems in order to find singularities of index 1 for vector fields with isolated zeroes in a 3-ball. The main result shows the existence of such singularities 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. Examples are given to motivate the hypotheses.
scientific article; zbMATH DE number 5380233