Geodesic
Finite-Dimensional Discrete Systems Integrated in Quadratures
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 422-436

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We consider finite-dimensional reductions (truncations) of discrete systems of the type of the Toda chain with discrete time that retain the integrability. We show that for finite-dimensional chains, in addition to integrals of motion, we can construct a rich family of higher symmetries described by the master symmetry. We reduce the problem of integrating a finite-dimensional system to the implicit function theorem.
Keywords: integrability, truncation condition, zero-curvature equation, classical symmetry, master symmetry, integrals of motion. 
@article{TMF_2004_138_3_a5,
     author = {T. G. Kazakova},
     title = {Finite-Dimensional {Discrete} {Systems} {Integrated} in {Quadratures}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {422--436},
     publisher = {mathdoc},
     volume = {138},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a5/}
}
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T. G. Kazakova. Finite-Dimensional Discrete Systems Integrated in Quadratures. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 422-436. http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a5/