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$% J. Olivares-Vázquez,
On vector fields in
without a separatrix, Rev. Mat. Univ. Complut. Madrid 5
(1992), no. 1, 13–34.%$
On Vector Fields in
without a Separatrix
A family of germs at
of holomorphic vector fields in
without separatrices
is constructed, with the aid of the blown-up foliation
in the blown-up
manifold
. We impose conditions on the multiplicity and the linear part of
at its singular points (i.e., non-semisimplicity and certain nonresonancy),
which are sufficient for the original vector field to be separatrix-free.
1991 Mathematics Subject Classification: 32L30.