Polynomial integrals of Hamiltonian systems with exponential interaction

ABSTRACT. The problem on the complete integrability of Hamiltonian systems with ex-ponential interaction is considered. These systems include, in particular, Toda chains and their generalizations. Conditions for the existence of a complete set of indepen-dent 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. 1