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

Abstract

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.

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

References in corpus (1)

• Double Elliptic Dynamical Systems From Generalized Mukai - Sklyanin Algebras

Cited by in corpus (2)

• Multi-Hamiltonian structures for r-matrix systems
• Integrable systems whose spectral curve is the graph of a function