Generic hyperelliptic Prym varieties in a generalized Henon-Heiles system

JOURNAL OF GEOMETRY AND PHYSICS

卷:87

Article

Enolski, V. Z.¹  Fedorov, Yu. N.²  Hone, A. N. W.³ 

[1] Univ Edinburgh, Sch Math, Edinburgh, Midlothian, Scotland

[2] Politech Univ Catalonia, Dept Math 1, Barcelona, Spain

[3] Univ Kent, Sch Math Stat & Actuarial Sci, Canterbury, Kent, England

关键词: Separation of variables;    Spectral curves;    Prym varieties;    Backlund transformation;   

DOI  :  10.1016/j.geomphys.2014.01.004

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier B.V. All rights reserved.

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