linear estimate of the number of zeros of abelian integrals for a kind of quintic hamiltonians
نویسندگان
چکیده
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 $2[frac{n-1}{2}]+1$.
منابع مشابه
LINEAR ESTIMATE OF THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A KIND OF QUINTIC HAMILTONIANS
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 $2[frac{n-1}{2}]+1$.
متن کاملlinear estimate of the number of zeros of abelian integrals for a kind of quintic hamiltonians
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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We consider the number of zeros of the integral I(h) = ∮ Γh ω of real polynomial form ω of degree not greater than n over a family of vanishing cycles on curves Γh : y 2 + 3x − x = 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[n−1 2 ] + 1.
متن کاملLinear Estimate of the Number of Zeros of Abelian Integrals for a Kind of Quartic Hamiltonians*
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عنوان ژورنال:
bulletin of the iranian mathematical societyجلد ۳۷، شماره No. ۲، صفحات ۱۰۱-۱۱۶
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