0809.0135 (Primitivo B. Acosta-Humanez et al.)

On Hamiltonian potentials with quartic polynomial normal variational
equations    [PDF]

Primitivo B. Acosta-Humanez, David Blazquez-Sanz, Camilo Vargas Contreras

In this paper we prove that there exists only one family of classical Hamiltonian systems of two degrees of freedom with invariant plane $\Gamma=\{q_2=p_2=0\}$ whose normal variational equation around integral curves in $\Gamma$ is generically a Hill-Schr\"odinger equation with quartic polynomial potential. In particular, by means of the Morales-Ramis theory, these Hamiltonian systems are non-integrable through rational first integrals.

View original: http://arxiv.org/abs/0809.0135