Geodesic
Polynomial integrals of Hamiltonian systems with exponential interaction
Izvestiya. Mathematics , Tome 34 (1990) no. 3, pp. 555-574.

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The problem on the complete integrability of Hamiltonian systems with exponential interaction is considered. These systems include, in particular, Toda chains and their generalizations. Conditions for the existence of a complete set of independent polynomial integrals are found. A complete classification of integrable systems is given by means of Dynkin diagrams. Certain new integrable chains are indicated. Bibliography: 20 titles. 
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V. V. Kozlov; D. V. Treschev. Polynomial integrals of Hamiltonian systems with exponential interaction. Izvestiya. Mathematics , Tome 34 (1990) no. 3, pp. 555-574. http://geodesic.mathdoc.fr/item/IM2_1990_34_3_a2/

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