Canonical perturbation theory, stability and diffusion in Hamiltonian systems: applications in dynamical astronomy

Abstract

This is a set of lecture notes on methods and techniques of canonical perturbation theory, as well as on the latter’s applications in the study of diffusion processes and chaos in physical systems related to dynamical astronomy. The text represents, to a considerable extent, an elaborated transcript of the lectures given by the author during the third La Plata school on Astronomy and Geophysics, in July 2011. However, the structure of the text, and in particular, the sequence of presentation of the topics, has been substantially modified with respect to the structure of the lectures. Also, the text has been enriched by a number of additional topics, reference to which was judged necessary for reasons of completeness.