quantity of order $\sim \eps$ leads to a big (of order $\sim 1$ compared with the typical values) relative change in the amplitude of the scattering. Hence, the scattering can be considered as a random process.

As the passages through the vicinity of a resonance lead to the destruction of adiabatic invariance of $\Ffi$, the structure of streamlines becomes chaotic. Note, that the expectation of the change of $\Ffi$ (the probability of a phenomenon times the size of a change of $\Ffi$) is of the same order for scattering and capture. Thus both processes contribute to the stochastization equally. There is a crucial difference between these resonant phenomena and certain other routes to chaos, like separatrix splitting. Although the total size of the resonant zone is small with the magnitude of the perturbation and it is localized in the space, the effect is large and global: the chaotic domain is of the order $1$ (of the order of the total size of the system) regardless of the magnitude of perturbation.

The description of motion in the vicinity of the resonance.
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Let us derive equations of motion in the vicinity of the resonant surface, that is called a [*resonant zone*]{}. 