On Hamiltonian potentials with quartic polynomial normal variational equations
Abstract
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 HillSchrödinger equation with quartic polynomial potential. In particular, by means of the MoralesRamis theory, these Hamiltonian systems are nonintegrable through rational first integrals.
 Publication:

arXiv eprints
 Pub Date:
 August 2008
 arXiv:
 arXiv:0809.0135
 Bibcode:
 2008arXiv0809.0135A
 Keywords:

 Mathematical Physics;
 37J30;
 12H05;
 70H07
 EPrint:
 12 pages