Geodesic
Cartan matrices in the~Toda--Darboux chain theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 1, pp. 22-29

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We discuss a one-to-one correspondence between the polynomial first integrals of Hamiltonian systems with exponential interaction and the hyperintegrals of the two-dimensional Toda lattice. We establish formulas for recalculating the corresponding polynomials and some general properties of their algebraic structure.
Mots-clés : Cartan matrix
Keywords: polynomial first integral, exponential system. 
@article{TMF_2018_196_1_a1,
     author = {A. B. Shabat and V. E. Adler},
     title = {Cartan matrices in {the~Toda--Darboux} chain theory},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {22--29},
     publisher = {mathdoc},
     volume = {196},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a1/}
}
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A. B. Shabat; V. E. Adler. Cartan matrices in the~Toda--Darboux chain theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 196 (2018) no. 1, pp. 22-29. http://geodesic.mathdoc.fr/item/TMF_2018_196_1_a1/