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Quadratic vanishing cycles, reduction curves and reduction of the monodromy group of plane curve singularities
The geometric monodromy of a plane curve singularity is a quasi-finite
diffeomorphism. In this paper we locate the reduction curves of the geometric
monodromy and the quadratic vanishing cycles of the singularity. An application
to the geometric monodromy group is given.Comment: 20 pages, 16 figure
Sub-normal Solutions to Painleve's Second Differential Equation
In a recent paper, Aimo Hinkkanen and Ilpo Laine proved that the
transcendental solutions to Painleve's second differential equation w"=a+zw+w^3
have either order of growth 3 or else 3/2. We complete this result by proving
that there exist no sub-normal solutions (order of growth 3/2) other than the
so-called Airy solutions
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