of the resonance-induced chaotic advection in Stokes flows. However, in many problems $\Ffi$ can only be obtained in a linearized form in the vicinity of a resonance. In the latter case we use the change of variables (\[vp3\]) to write (\[vp5b\]) as = -2 s \_[-s ]{}\^[\_\*]{} ( f\_[1,0]{} + f\_[2,0]{} ) d. \[vp6\] Define the quantity $\xi$ as $$\xi = \{ \dfrac{h_*}{2\pi \left| a \right|} \},$$ where the curly brackets denote the fractional part. In terms of $\xi$, (\[vp6\]) can be written as = -2 s 1 \_[-s ]{}\^[\_\*]{} 1 ( f\_[1,0]{} + f\_[2,0]{} ) d. \[vp6a\] The quantity $\xi$ characterizes a scattering. For every set of initial conditions, the values of $\xi$ and $\Dt \Ffi$ can be calculated exactly. However, a small change of order $\eps$ in the initial conditions produces in general a large change of order $1$ in $\xi$. Hence for small $\eps$ it is the best to treat $\xi$ as a random variable, uniformly distributed on $(0,1)$ (see [@Neishtadt:1999]).

Statistical properties of the scatterings depend on the shape of the phase portrait on the $(\th,
\th^{\pr})$ plane. If the phase portrait looks like the one shown in Fig. 1a, in a generic case, scatterings on 