Apply change of variables $$\left(I_1, I_2\right) \to \left(\sg, \om \right),$$ such that - = (I\_1, I\_2), \[vp3\] where $\om$ is the angular velocity defined above, $\sg$ is an additional variable (chosen in such a way that (\[vp3\]) is satisfied) and $\mu(I_1, I_2)$ is a coefficient in the expression for the infinitesimal volume: $d V = \mu(I_1, I_2) dI_1 dI_2 d \th$. Actually, (\[vp3\]) can be relaxed to be required on ${\mit R}$ only. In terms of the new variables equations of motion (\[vp1\]) can be written as &=& f\_1( , , ),\
&=& f\_2( , , ), \[vp4\]\
&=& + g( , , ). and the divergence-free condition has the most simple form: $$\frac{\pt f_1}{\pt \om} + \frac{\pt f_2}{\pt \sg} + \frac{\pt g}{\pt \th} =0.$$ In the resonance zone we have: &=& f\_1( , , ) + + O(\^2)\
&=& . f\_1( , , )|\_[=0]{} + ( + ) + O(\^2)\
&=& f\_1( 0, , ) + ( + ) + O(\^2)\
&=& f\_1( 0, , ) - + O(\^2). It follows from the last line in the above equation that the width of the resonant zone is given by $\left| \dot\th \right| < \const \sqrt{\eps}$. Rescaling time, $$\tau = 