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. 
V.Z. Enolski, Yu.N.Fedorov and A.N.W. Hone
nlin.SI math.AG