Some applications of moser's twist theorem

The modest goal of this chapter is to present to non-specialists some examples of physically relevant dynamical systems where KAM theory applies, sometimes in a way that is not immediately apparent. For a much broader view of the subject we refer to the tutorial [14] which in turn contains numerous references to literature. The present article concentrates on specific examples, mostly in low dimensions. The main difficulty in these problems lies in reducing the problem into a form to which the theory is readily applicable. This article is not meant to be a survey of applications, but rather is a sample designed to give a flavour of some of the applications. The most glaring omission is the application to celestial mechanics; we refer to [18] for a discussion of the n-body problem and for further references. For further reading we refer the reader to [28,41,42,46,54].