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

Document Type: Other

Authors

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

Keywords

### History

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