Chaotic diffusion on periodic orbits and uniformity

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnolʹd cat map, exhibiting a transition from uniform to nonuniform hyperbolicity as the perturbation parameter is increased. The results for the diffusion coefficient from PO formulas agree very well with those obtained by standard methods. Using the original PO formula involving a uniform (nonweighted) average over the POs, reasonably accurate results are obtained for sufficiently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to uniformity sum rules satisfied by the PO Lyapunov eigenvalues at fixed winding number.