Linear estimate for the number of zeros of Abelian integrals

2009/03/29 by Malev, S. G., Novikov, D.
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0903.5056

Abstract

We prove a linear in degω upper bound on the number of real zeros of the Abelian integral I(t)=∫_δ(t)ω, where δ(t)⊂\R² is the real oval x²y(1-x-y)=t and ω is a one-form with polynomial coefficients.

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