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Paper detail

Generic hyperelliptic Prym varieties in a generalized Henon-Heiles system

It is known that the Jacobian of an algebraic curve which is a 2-fold covering of a hyperelliptic curve ramified at two points contains a hyperelliptic Prym variety. Its explicit algebraic description is applied to some of the integrable Henon-Heiles systems with a non-polynomial potential. Namely, we identify the generic complex invariant manifolds of the systems as a hyperelliptic Prym subvariety of the Jacobian of the spectral curve of the corresponding Lax representation. The exact discretization of the system is described as a translation on the Prym variety.

preprint2014arXivOpen access
V. Z. EnolskiYu. N. FedorovA. N. W. Hone
math.AGnlin.SI
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V. Z. EnolskiYu. N. FedorovA. N. W. Hone

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