POLYNOMIAL INTEGRALS OF HAMILTONIAN SYSTEMS WITH EXPONENTIAL INTERACTION

V V Kozlov, D V Treshchev
1990 Mathematics of the USSR-Izvestiya  
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.
doi:10.1070/im1990v034n03abeh000670 fatcat:gwdgyxttkbcvndnf7tglnnktfm