SUBHARMONIC ORBITS IN AN ANHARMONIC-OSCILLATOR

In a recent paper, Christie and Gopalsamy [2] used Melnikov's method t o establish a sufficient condition for the existence of chaotic behavi our, in the sense of Smale, in a particular time-periodically perturbe d planar autonomous system of ordinary differential equations. They th en concluded with an application to the dynamics of a one-dimensional anharmonic oscillator. In this paper, the same system is considered an d a condition for the existence of subharmonic orbits in the perturbed system is deduced, using the subharmonic Melnikov theory. Finally, an application is given to the dynamical behaviour of the one-dimensiona l anharmonic oscillator system.