Abstract:
We calculate the second term of the asymptotics of the
monodromy transformation of a monodromic
singular point of an analytic vector field on a plane
whose Newton diagram consists of one or two edges.
In the cases under consideration the principal term
of the monodromy transformation coincides
with the identity function. The case of two edges is
characterized by the fact that,
as a result of blowing up the singularity by the Newton diagram,
a singular point emerges that is a degenerate saddle.
The results obtained make it possible to state a sufficient condition
for the existence of a focus and to construct the
stability boundary in the classes of vector fields under consideration.
Keywords:monodromic singular point, blowing up singularities, focus, centre, monodromy transformation.
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