Geodesic
Generalized Legendre transformations
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 2, pp. 179-194 Cet article a éte moissonné depuis la source Math-Net.Ru

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We discuss a general theory of the integrable Toda lattices which are considered as Lagrangian dynamical systems with one continuous and one discrete time. The invariance with respect to an analog of the classical Legendre transformations implies their integrability. 
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V. E. Adler; A. B. Shabat. Generalized Legendre transformations. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 2, pp. 179-194. http://geodesic.mathdoc.fr/item/TMF_1997_112_2_a0/

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