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.

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.

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.

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, 2011; 37(No. 2): 101-116.

LINEAR ESTIMATE OF THE NUMBER OF ZEROS OF
ABELIAN INTEGRALS FOR A KIND OF QUINTIC
HAMILTONIANS

Receive Date: 03 October 2008,
Revise Date: 15 November 2008,
Accept Date: 16 November 2008

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 $2[frac{n-1}{2}]+1$.