DIFFUSION ON THE TORUS FOR HAMILTONIAN MAPS

For a mapping of the torus T2 we propose a definition of the diffusion coefficient D suggested by the solution of the diffusion equation on T2. The definition of D, based on the limit of moments of the invariant measure, depends on the set OMEGA where an initial uniform distribution is assigned. For the algebraic automorphism of the torus the limit is proved to exist and to have the same value for almost all initial sets OMEGA in the subfamily of parallelograms. Numerical results show that it has the same value for arbitrary polygons Q and for arbitrary moments.