@Article{karney83c,
author = {Charles F. F. Karney},
title = {Long-Time Correlations in the Stochastic Regime},
journal = {Physica},
volume = {8D},
number = 3,
pages = {360-380},
month = sep,
year = 1983,
reprint = {physd83b},
note = {Reprinted in {\em Hamiltonian Dynamical Systems},
edited by R. S. MacKay and J. D. Meiss (Adam-Hilger,
Bristol, 1987), pages 585--605},
preprint = {Princeton Univ. Rept. PPPL--1938 (Nov. 1982) 40 pp.},
eprint = {nlin.CD/0501023},
doi = {10.1016/0167-2789(83)90232-4},
abstract = {The phase space for Hamiltonians of two degrees of
freedom is usually divided into stochastic and
integrable components. Even when well into the
stochastic regime, integrable orbits may surround
small stable regions or islands. The effect of these
islands on the correlation function for the stochastic
trajectories is examined. Depending on the value of
the parameter describing the rotation number for the
elliptic fixed point at the center of the island, the
long-time correlation function may decay as
<i>t</i> <sup>−5</sup> or exponentially,
but more commonly it decays much more slowly (roughly
as <i>t</i> <sup>−1</sup>). As a
consequence these small islands may have a profound
effect on the properties of the stochastic orbits. In
particular, there is evidence that the evolution of a
distribution of particles is no longer governed by a
diffusion equation.}
}