Long-time correlations and expansion-rate spectra of chaos in Hamiltonian systems

The repeated sticking of a chaotic orbit to critical tori with an inverse-power distribution of sticking times is shown to produce a universal spectrum of expansion rates Λ of nearby orbits with a linearity with zero slope for 0<Λ<Λ∞ (=Liapunov number), representing the intermittent switching between chaotic sea and chaos border. In this paper, chaos in conservative systems was discussed from such a new viewpoint by showing results of numerical experiments for the standard map. (M.T.)