Linear estimate for the number of zeros of Abelian integrals

Details Linear estimate for the number of zeros of Abelian integrals Linear estimate for the number of zeros of Abelian integrals

2009-03-29

arxiv.org/abs/0903.5056v1

Mathematics

Differential Geometry

Scientific paper

We prove a linear in $\deg\omega$ upper bound on the number of real zeros of
the Abelian integral $I(t)=\int_{\delta(t)}\omega$, where
$\delta(t)\subset\R^2$ is the real oval $x^2y(1-x-y)=t$ and $\omega$ is a
one-form with polynomial coefficients.

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