Linear estimate for the number of zeros of Abelian integrals

Mathematics – Differential Geometry

Scientific paper

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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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