Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1892762 | Journal of Geometry and Physics | 2015 | 9 Pages |
Abstract
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 Hénon–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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
V.Z. Enolski, Yu.N. Fedorov, A.N.W. Hone,