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arXiv · 0903.5056

Linear estimate for the number of zeros of Abelian integrals

S. G. Malev·D. Novikov
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Abstract

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

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S. G. Malev, D. Novikov. 2009-03-29. Linear estimate for the number of zeros of Abelian integrals. https://arxiv.org/abs/0903.5056

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