Symmetric Liapunov center theorem for orbit with nontrivial isotropy group

Marta Kowalczyk, Ernesto Pérez-Chavela, Sławomir Rybicki

In this article we prove two versions of the Liapunov center theorem for symmetric potentials. We consider a~second order autonomous system $\ddot{q}(t)=-\nabla U(q(t))$ in the pres…