On Hamiltonian potentials with quartic polynomial normal variational equations

Details On Hamiltonian potentials with quartic polynomial normal variational equations On Hamiltonian potentials with quartic polynomial normal variational equations

2008-08-31

arxiv.org/abs/0809.0135v2

Nonlinear studies, Vol 16, No 3 (2009)

Physics

Mathematical Physics

12 pages

Scientific paper

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.

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