Yu. N. Bibikov
Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia,
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics,
Differential Equations Department
A problem of the stability of the state of equilibrium of Hamiltonian systems with two degrees of freedom is considered. Systems under consideration describe motions of slightly coupled oscillators whose restoring forces are of odd degree. It is proved that if the restoring forces are not equal to each other, then the state of equilibrium is Liapunov stable. If they are equal to each other, then the case of the stability is generic.