Vector fields with a given set of singular points

Details Vector fields with a given set of singular points Vector fields with a given set of singular points

1999-01-26

arxiv.org/abs/math/9901116v1

Ukrainian Mathematical Journal, Vol. 49, No. 10, 1997, 1373-1384

Mathematics

Dynamical Systems

Scientific paper

Theorems on the existence of vector fields with given sets of Indexes of
isolated Singular points are proved for the cases of closed manifolds, pairs of
manifolds, manifolds with boundary, and gradient fields. It is proved that, on
a two-dimensional manifold, an index of an isolated Singular point of the
gradient field is not greater than one.

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