A resonance model on a cylinder

Various phenomena of resonances and bifurcations are explained by one-param eter models made of a simple pendulum under perturbation. The model we brin g here involves two parameters, and thus covers more generic situations tha n the simple pendulum. The solutions are exact; they are expressed in ellip tic functions. Periodic perturbations of the model, however, can be treated by the method of Howland-Henrard-Wauthier. (C) 2001 Elsevier Science Ltd. All rights reserved.