linear estimate of the number of zeros of abelian integrals for a kind of quintic hamiltonians

Authors

n. nyamoradi

h. zangeneh

abstract

we consider the number of zeros of the integral $i(h) = oint_{gamma_h} omega$ of real polynomial form $omega$ of degree not greater than $n$ over a family of vanishing cycles on curves $gamma_h:$ $y^2+3x^2-x^6=h$, where the integral is considered as a function of the parameter $h$. we prove that the number of zeros of $i(h)$, for $0 < h < 2$, is bounded above by $2[frac{n-1}{2}]+1$.

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Journal title:
bulletin of the iranian mathematical society

جلد ۳۷، شماره No. ۲، صفحات ۱۰۱-۱۱۶

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