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On two nonintegrable cases of the generalized Henon-Heiles system with an additional nonpolynomial term

E. I. Timoshkova·S. Yu. Vernov
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Abstract

The generalized Henon-Heiles system with an additional nonpolynomial term is considered. In two nonintegrable cases new two-parameter solutions have been obtained in terms of elliptic functions. These solutions generalize the known one-parameter solutions. The singularity analysis shows that it is possible that three-parameter single-valued solutions exist in these two nonintegrable cases. The knowledge of the Laurent series solutions simplifies search of the elliptic solutions and allows to automatize it.

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E. I. Timoshkova, S. Yu. Vernov. 2004-02-18. On two nonintegrable cases of the generalized Henon-Heiles system with an additional nonpolynomial term. https://doi.org/10.1134/1.2131124

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