Separation of Variables and the Geometry of Jacobians

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 05 Feb 2007Embargo end date: 01 Feb 2007Publisher:SIGMA (Symmetry, Integrability and Geometry: Methods and Application)Journal:Symmetry, Integrability and Geometry: Methods and Applications (eissn: 1815-0659,

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Authors: Hurtubise, J.;

doi: 10.3842/sigma.2007.017 , 10.48550/arxiv.math-ph/0702032

arXiv: math-ph/0702032

Separation of Variables and the Geometry of Jacobians

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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.

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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Keywords

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests, Nonlinear Sciences - Exactly Solvable and Integrable Systems, separation of variables, FOS: Physical sciences, Riemann surfaces; Weierstrass points; gap sequences, Mathematical Physics (math-ph), Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics, Riemann surfaces, Mathematics - Algebraic Geometry, integrable Hamiltonian systems, QA1-939, FOS: Mathematics, Exactly Solvable and Integrable Systems (nlin.SI), Algebraic Geometry (math.AG), geometry of Jacobians, Mathematics, Mathematical Physics

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