resonance, or crosses the resonant zone without being captured. (Actually, there is also some intermediate regime of motion in the resonant zone, but it occurs for a very small measure of initial conditions; we will not discuss it.) Phenomenologically, the difference between the two regimes of motion in the resonant zone can be described as follows. In the case of capture, upon the arrival to the resonant zone the phase $\th$ switches its behavior from rotation ($\th$ changes monotonically, a streamline makes full circles around the axis) to oscillation ($\th$ changes between two values, $\dot{\th}$ changes the sign twice during each period). In the case of crossing the resonant zone without capture, $\dot{\th}$ changes the sign only once in the resonant zone. As we show below, the two phenomena have qualitatively different impact on the streamlines’ behavior. After the passage through the resonant zone (and far from the resonance) the value of $\Ffi$ oscillates near some other value, $\Ffi^+$, again with a small amplitude $\sim \eps$.

In the rest of the present section we provide a qualitative description of these phenomena (without any proofs) and return to a detailed quantitative description in the next section.

In the case of capture 