Canonical structure and symmetries of the Schlesinger equations

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dc.creatorDubrovin, Boris
dc.creatorMazzocco, Marta
dc.date2003-11-16
dc.date2007-01-10
dc.date.accessioned2026-07-07T07:39:24Z
dc.date.available2026-07-07T07:39:24Z
dc.descriptionThe Schlesinger equations $S_{(n,m)}$ describe monodromy preserving deformations of order $m$ Fuchsian systems with $n+1$ poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of $n$ copies of $m\times m$ matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation of the general Schlesinger equations $S_{(n,m)}$ for all $n$, $m$ and we compute the action of the symmetries of the Schlesinger equations in these coordinates.
dc.description92 pages, no figures. Theorem 1.2 corrected, other misprints removed. To appear on Comm. Math. Phys
dc.identifierhttps://arxiv.org/abs/math/0311261
dc.identifierhttp://arxiv.org/abs/math/0311261
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121435
dc.subjectDifferential Geometry
dc.subjectClassical Analysis and ODEs
dc.subjectExactly Solvable and Integrable Systems
dc.subject32G34 (Primary); 34M55, 53D30 (Secondary)
dc.titleCanonical structure and symmetries of the Schlesinger equations
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