On the conditions of total resonance of Liouville type Hamiltonian systems with $n$ degrees of freedom

The completely singular dynamical systems of the Liouville type are studied. The motion paths of these systems are closed graphs if the Liouville tori are compact. The conditions under which a dynamical system of the Liouville type is strongly singular are obtained in the paper. These conditions have a form of the system of integral equations. It is proved that the obtained system is solvable.