The isolated generating periodic solutions to the Beletsky equation

We study degeneracies in families of periodic solutions to the Beletsky equation which correspond to intersections of three manifolds of these solutions: the symmetric, the asymmetric ones, and the manifold belonging to one of the integrable cases, i.e. $e=0$ or $\mu=0$. We obtained equations for these isolated solutions, which allow to compute them with an arbitrary precision. It is shown that additional degeneracies take place in some of these solutions. The method we use is applicable to the wide class of nonlinear ODEs depending on parameters.