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Nonintegrability of a system of interacting particles with the Dyson potential. (English. Russian original) Zbl 0972.70016
Dokl. Math. 59, No. 3, 485-486 (1999); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 366, No. 1, 30-31 (1999).
This paper deals with the integrability of the dynamic system of $$n$$ interacting particles with the Dyson potential $$V(z)= \ln|\sin z|$$. The authors analyze the problem by using previous results by V. V. Kozlov. In the complex variables setting, they find that the system has only one single-valued polynomial first integral.

##### MSC:
 70H07 Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics 70F10 $$n$$-body problems 37J30 Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) 37N05 Dynamical systems in classical and celestial mechanics