On the Homoclinic Orbits in a Class of Two-Degree-of-Freedom Systems under the Resonance Conditions

A class of two-degree-of-freedom systems in resonance with an external, parametric excitation is investigated, the existence of the periodic solutions locked to Ω is proved by the use of the method of multiple scales. This systems can be transformed into the systems of Wiggins under some conditions. A calculating formula which determines the existence of homoclinic orbits of the systems is given. Foundation item: the National Natural Science Foundation of China (19872044) Biography: WANG Mao-nan (1965-)