Generic hyperelliptic Prym varieties in a generalized Henon-Heiles system
Exactly Solvable and Integrable Systems
2015-06-18 v1 Algebraic Geometry
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 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.
Keywords
Cite
@article{arxiv.1402.1102,
title = {Generic hyperelliptic Prym varieties in a generalized Henon-Heiles system},
author = {V. Z. Enolski and Yu. N. Fedorov and A. N. W. Hone},
journal= {arXiv preprint arXiv:1402.1102},
year = {2015}
}