MONOTONICITY OF THE RATIO OF TWO ABELIAN INTEGRALS FOR A CLASS OF SYMMETRIC HYPERELLIPTIC HAMILTONIAN SYSTEMS

Abstract

In this paper we study the monotonicity of the ratio of two hyperelliptic Abelian integrals I0(h)=∮Γh ydx and I1(h)=∮Γh xydx for which Γh is a continuous family of periodic orbits of a Newtonian system with Hamiltonian function of the form H(x,y)=1/2 y2 ±Ψ(x), where Ψ is an arbitrary even function of degree six.