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 $2[frac{n-1}{2}]+1$.
NYAMORADI, N., & ZANGENEH, H. (2011). LINEAR ESTIMATE OF THE NUMBER OF ZEROS OF
ABELIAN INTEGRALS FOR A KIND OF QUINTIC
HAMILTONIANS. Bulletin of the Iranian Mathematical Society, 37(No. 2), 101-116.
MLA
NYAMORADI, N., & ZANGENEH, H. "LINEAR ESTIMATE OF THE NUMBER OF ZEROS OF
ABELIAN INTEGRALS FOR A KIND OF QUINTIC
HAMILTONIANS", Bulletin of the Iranian Mathematical Society, 37, No. 2, 2011, 101-116.
HARVARD
NYAMORADI N., ZANGENEH H. (2011). 'LINEAR ESTIMATE OF THE NUMBER OF ZEROS OF
ABELIAN INTEGRALS FOR A KIND OF QUINTIC
HAMILTONIANS', Bulletin of the Iranian Mathematical Society, 37(No. 2), pp. 101-116.
CHICAGO
N. NYAMORADI & H. ZANGENEH, "LINEAR ESTIMATE OF THE NUMBER OF ZEROS OF
ABELIAN INTEGRALS FOR A KIND OF QUINTIC
HAMILTONIANS," Bulletin of the Iranian Mathematical Society, 37 No. 2 (2011): 101-116,
VANCOUVER
NYAMORADI N., ZANGENEH H. LINEAR ESTIMATE OF THE NUMBER OF ZEROS OF
ABELIAN INTEGRALS FOR A KIND OF QUINTIC
HAMILTONIANS. BIMS. 2011;37(No. 2):101-116.
