Chaotic diffusion in multidimensional Hamiltonian systems

PABLO CINCOTTA; CLAUDIA GIORDANO

Sao José dos Campos

Congreso; International Conference on Chaos and Non Linear Dynamics: Dynamics Days in South America 2010; 2010

INPE

General diffusion in phase space (not Arnol´d diffusion) or what we have called Arnol´d diffusion-like transport processes (in a geometrical sense), is thoroughly discussed in this presentation by dealing with a 4-dimensional conservative map that would be representative of the dynamics of resonance interaction, the so-called the coupled rational shifted standard map. The computation of the standard random walk diffusion-like coefficient, defined through the variance of the unperturbed action variables, is used as a first approach to measure the extent of variation of the unperturbed integrals, provides relatively confident results. Alternatively, we consider the finite time Shannon or Arnol´d entropy as an alternative way to heuristically measure the variation of local or global integrals of motion. We find that both measures of diffusion reveal as an alternative dynamical indicators, but they provide more information about the dynamics of the system with less computational effort, since it is not necessary to solve variational equations, just the Hamiltonain flow.