Diffusion models in strongly chaotic Hamiltonian systems

Abstract

The main subject of this thesis is the long time behaviour of strongly chaotic Hamiltonian systems and whether their behaviour ran be modelled with diffusion processes. The problem of diffusion caused by chaos in a particular area preserving map on the torus, the web map is studied. The formalism is then generalised for the study of diffusion in higher dimensional symplectic maps on the cylinder and general results are obtained. A numerical method for the calculation of diffusion coefficients for chaotic maps is described. Finally, the problem of diffusion in phase space in the case where chaos coexists with structures such as stable islands is studied