Diffusion in multidimensional Hamiltonian Systems Application to Galactic Dynamics

Abstract

In the present lectures we provide results and discussions concerning the processes that lead to local and global chaotic diffusion in phase space of multidimensional conservative systems. We investigate and provide a measure of the extent of the domain over which diffusion may occur. All these issues are thoroughly discussed by dealing with a toy model such as the perturbed quartic oscillator as well as with a multidimensional conservative map that would be representative of the dynamics of a resonance interaction, which is an important mechanism in several astronomical systems, like the Solar System or galaxies. Most of the contents of the present lectures are based on previous works of the authors already published in several journals.