Symmetry and Resonance in Hamiltonian Systems

@article{Verhulst2001SymmetryAR,
  title={Symmetry and Resonance in Hamiltonian Systems},
  author={Ferdinand Verhulst and J. M. Tuwankotta},
  journal={SIAM J. Appl. Math.},
  year={2001},
  volume={61},
  pages={1369-1385}
}
In this paper we study resonances in two degrees of freedom, autonomous, Hamiltonian systems. Due to the presence of a symmetry condition on one of the degrees of freedom, we show that some of the resonances vanish as lower order resonances. After giving a sharp estimate of the resonance domain, we investigate this order change of resonance in a rather general potential problem with discrete symmetry and consider as an example the Henon--Heiles family of Hamiltonians. We also study a classical… 

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