DIFFUSION IN VERY CHAOTIC HAMILTONIAN SYSTEMS

We study nonintegrable Hamiltonian dynamics: H(I,{theta}}) = H{sub 0}(I)+kH{sub 1}(I,{theta}) for large k; that is, far from integrability. An integral representation is given for the conditional probability P(I,{theta},t|I{sub 0},{theta}{sub 0},t{sub 0}) that the system is at I,{theta} at t, given it was at I{sub 0},{theta}{sub 0} at t{sub 0}. By discretizing time into steps of size {epsilon}, we show how to evatuate physical observables for large k, fixed {epsilon}. An explicit calculation of a diffusion coefficient in a two degree of freedom problem is reported. Passage to {epsilon} = 0, the original Hamiltonian flow, discussed