Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 017, 14 pages      math-ph/0702032      http://dx.doi.org/10.3842/SIGMA.2007.017
Contribution to the Vadim Kuznetsov Memorial Issue

Separation of Variables and the Geometry of Jacobians

Jacques Hurtubise
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. W. Montreal H3A 2K6, Canada

Received November 17, 2006, in final form January 08, 2007; Published online February 05, 2007

Abstract
This survey examines separation of variables for algebraically integrable Hamiltonian systems whose tori are Jacobians of Riemann surfaces. For these cases there is a natural class of systems which admit separations in a nice geometric sense. This class includes many of the well-known cases.

Key words: separation of variables; integrable Hamiltonian systems; geometry of Jacobians.

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