Geodesic
Generalized Legendre transformations
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 2, pp. 179-194

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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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     author = {V. E. Adler and A. B. Shabat},
     title = {Generalized {Legendre} transformations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--194},
     publisher = {mathdoc},
     volume = {112},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_112_2_a0/}
}
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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/