Hamiltonians with two degrees of freedom admitting a singlevalued general solution

@article{Conte2005HamiltoniansWT,
  title={Hamiltonians with two degrees of freedom admitting a singlevalued general solution},
  author={Robert Conte and Micheline Musette and Caroline Verhoeven},
  journal={Analysis in Theory and Applications},
  year={2005},
  volume={21},
  pages={188-200}
}
AbstractFollowing the basic principles stated by Painlevé, we first revisit the process of selecting the admissible time-independent Hamiltonians H=(p12+p22)/2+V(q1, q2) whose some integer power $$q_j^{n_j } (t)$$ of the general solution is a singlevalued function of the complex time t. In addition to the well known rational potentials V of Hénon-Heiles, this selects possible cases with a trigonometric dependence of V on qj. Then, by establishing the relevant confluences, we restrict the… CONTINUE READING

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