Explicit integration of the system of invariant relations for the case of M. Adler and P. van Moerbeke

Resumo

For the general integrability case of M. Adler and P. van Moerbeke, invariant relations are obtained in which the rank of the momentum map is 1. Thereby, special periodic solutions generating the edges of the bifurcation diagram are defined. All phase variables are expressed in terms of a set of constants and one auxiliary variable, for which a differential equation integrable in elliptic functions time is given. An explicit expression for the characteristic exponent determining the type of special periodic solutions is presented, which makes it possible to study the character of stability of the obtained solution.