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dc.contributor.authorFedorov, Yuri
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.description.abstractThere is a wide class of integrable Hamiltonian systems on finite-dimensional coadjoint orbits of the loop algebra ˜ gl(r) which are represented by r × r Lax equations with a rational spectral parameter.A reduced complex phase space is foliated with open subsets of Jacobians of regularized spectral curves.Under some generic restrictions on the structure of the Lax matrix, we propose an algebraic geometrical scheme of a discretization of such systems that preserve their first integrals and is represented as translations on the Jacobians.A generic discretizing map is given implicitly in the form of an intertwining relation (a discrete Lax pair) with an extra parameter governing the translation.Some special cases when the map is explicit are also considered.As an example, we consider a modified discrete version of the classical Neumann system described by a 2 × 2 discrete Lax pair and provide its theta-functional solution.
dc.format.extent18 pages
dc.rightsAttribution-NonCommercial-NoDerivs 2.5 Spain
dc.subject.lcshDifference equations
dc.subject.lcshHamiltonian systems
dc.subject.otherLoop Algebra
dc.titleBacklund transformations on coadjoint orbits of the loop algebra gl(n)
dc.subject.lemacEquacions en diferències
dc.subject.lemacHamilton, Sistemes de
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.subject.amsClassificació AMS::39 Difference and functional equations::39A Difference equations
dc.rights.accessOpen Access

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