causes the invariants of the base flow to change and a result flow has the following form: \_1 &=& v\_1( I\_1, I\_2, ),\
\_2 &=& v\_2( I\_1, I\_2, ), \[vp1\]\
&=& ( I\_1, I\_2 ) + g( I\_1, I\_2 , ). System (\[vp1\]) is volume-preserving if the right hand side is divergence-free. For $0< \eps \ll
1$ flow (\[vp1\]) possesses two time scales. The variable $\th$ is fast and the variables $I_1$ and $I_2$ are slow with a ratio of characteristic velocities being of order of $\eps$. System (\[vp1\]) is an example of so-called slow-fast systems. Therefore, in the first approximation we can average velocity field (\[vp1\]) over the fast variable $\th$. It is clear that this approximation is valid everywhere except for a small part of the space where $\dot \th \apx 0$. The averaging over $\th$ reduces (\[vp1\]) to \_1 &=& 1[2]{}\_0\^[2]{} v\_1( I\_1, I\_2, ) d,\
\[vp2\]\
\_2 &=& 1[2]{}\_0\^[2]{} v\_2( I\_1, I\_2, ) d. For the sake of brevity, in (\[vp2\]) we used the same notation for $I_1$ and $I_2$ as in (\[vp1\]). System (\[vp2\]) is 2-D volume-preserving and, therefore, Hamiltonian and integrable. The Hamiltonian $\Ffi(I_1, I_2)$ is the flux of the perturbation vector ${\bf v} 