On Hamiltonian potentials with quartic polynomial normal variational equations

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

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 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.
Published
2009-08-13
Section
Articles