Geodesic
Nonautonomous Hamiltonian systems related to higher Hitchin integrals
Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 2, pp. 237-263 
A. M. Levin; M. A. Olshanetsky. Nonautonomous Hamiltonian systems related to higher Hitchin integrals. Teoretičeskaâ i matematičeskaâ fizika, Tome 123 (2000) no. 2, pp. 237-263. http://geodesic.mathdoc.fr/item/TMF_2000_123_2_a6/
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     author = {A. M. Levin and M. A. Olshanetsky},
     title = {Nonautonomous {Hamiltonian} systems related to higher {Hitchin} integrals},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {237--263},
     year = {2000},
     volume = {123},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_123_2_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We describe nonautonomous Hamiltonian systems derived from the Hitchin integrable systems. The Hitchin integrals of motion depend on $\mathcal W$-structures of the basic curve. The parameters of the $\mathcal W$-structures play the role of times. In particular, the quadratic integrals depend on the complex structure (the $\mathcal W_2$-structure) of the basic curve, and the times are coordinates in the Teichmьller space. The corresponding flows are the monodromy-preserving equations such as the Schlesinger equations, the Painlevé VI equation, and their generalizations. The equations corresponding to the higher integrals are the monodromy-preserving conditions with respect to changing the $\mathcal W_k$-structures $(k>2)$. They are derived by the symplectic reduction of a gauge field theory on the basic curve interacting with the $\mathcal W_k$-gravity. As a by-product, we obtain the classical Ward identities in this theory.

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