Corpus ID: 244282

On Hamiltonian potentials with cuartic polynomial normal variational equations

@article{AcostaHumnez2008OnHP,
  title={On Hamiltonian potentials with cuartic polynomial normal variational equations},
  author={P. Acosta-Hum{\'a}nez and D. Bl{\'a}zquez-Sanz and Camilo Vargas Contreras},
  journal={arXiv: Mathematical Physics},
  year={2008}
}
Here we find the complete family of two degree of freedom classical Hamiltonians with invariant plane $\Gamma=\{q_2=p_2=0\}$ whose normal variational equation around integral curves in $\Gamma$ is a generically a Hill-Schr\"odinger equation with cuartic polynomial potential. In particular, these Hamiltonian form a family of non-integrable Hamiltonians through rational first integrals. 

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