四次多项式正规变分方程的Hamilton势
On Hamiltonian potentials with quartic polynomial normal variational equations
摘要：
本文证明了仅存在一族具有不变平面$Γ=\{q_2=p_2=0\}$的两自由度经典Hamilton系统，其在$Γ$中积分曲线周围的法向变分方程一般是具有四次多项式势的Hill-薛定谔方程。特别地，通过Morales-Ramis理论，这些哈密顿系统通过有理第一积分不可积。
英文摘要：
In this paper we prove that there exists only one family of classical Hamiltonian systems of two degrees of freedom with invariant plane $Γ=\{q_2=p_2=0\}$ whose normal variational equation around integral curves in $Γ$ is generically a Hill-Schrödinger equation with quartic polynomial potential. In particular, by means of the Morales-Ramis theory, these Hamiltonian systems are non-integrable through rational first integrals.
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