| Volume 8, Number 1, 2018, Pages 344-355 DOI：10.11948/2018.344 |
| Monotonicity of the ratio of two Abelian integrals for a class of symmetric hyperelliptic Hamiltonian systems |
| Rasool Kazemi |
| Keywords:Hamiltonian system, hyperelliptic Abelian integral, monotonicity, asymptotic expansion. |
| Abstract: |
| In this paper we study the monotonicity of the ratio of two hyperelliptic Abelian integrals $I_0(h)=\oint_{\Gamma_h}ydx$ and $I_1(h)=\oint_{\Gamma_h}xydx$ for which $\Gamma_h$ is a continuous family of periodic orbits of a Newtonian system with Hamiltonian function of the form $H(x,y)=\frac{1}{2}{y^2}\pm \Psi(x)$, where $\Psi$ is an arbitrary even function of degree six. |
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