An integrable system on the moduli space of rational functions and its variants

Details An integrable system on the moduli space of rational functions and its variants An integrable system on the moduli space of rational functions and its variants

2002-02-20

arxiv.org/abs/nlin/0202042v2

Journal of Geometry and Physics 47 (1) (2003), 1-20

Nonlinear Sciences

Exactly Solvable and Integrable Systems

25 pages, AMS-LaTeX, no figure; minor changes

Scientific paper

We study several integrable Hamiltonian systems on the moduli spaces of meromorphic functions on Riemann surfaces (the Riemann sphere, a cylinder and a torus). The action-angle variables and the separated variables (in Sklyanin's sense) are related via a canonical transformation, the generating function of which is the Abel-Jacobi type integral of the Seiberg-Witten differential over the spectral curve.

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