Generic hyperelliptic Prym varieties in a generalized Henon-Heiles system

作者：Enolski V Z; Fedorov Yu N^*; Hone A N W

来源：Journal of Geometry and Physics, 2015, 87: 106-114.

DOI：10.1016/j.geomphys.2014.01.004

• Separation of variables
• Spectral curves
• Prym varieties
• Backlund transformation

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.

• 出版日期2015-1