  This article studies typical dynamics and fluctuations for a slow-fast
dynamical system perturbed by a small fractional Brownian noise. Based on an
ergodic theorem with explicit rates of convergence, which may be of independent
interest, we characterize the asymptotic dynamics of the slow component to two
orders (i.e., the typical dynamics and the fluctuations). The limiting
distribution of the fluctuations turns out to depend upon the manner in which
the small-noise parameter is taken to zero relative to the scale-separation
parameter. We study also an extension of the original model in which the
relationship between the two small parameters leads to a qualitative difference
in limiting behavior. The results of this paper provide an approximation, to
two orders, to dynamical systems perturbed by small fractional Brownian noise
and subject to multiscale effects.
