Chirikov criterion

The Chirikov criterion or Chirikov resonance-overlap criterion
was established by the Russian physicist Boris Chirikov.
Back in 1959, he published a seminal article,
where he introduced the very first physical criterion for the onset of chaotic motion in 
deterministic Hamiltonian systems. He then applied such a criterion to explain
puzzling experimental results on plasma confinement in magnetic bottles
obtained by Rodionov at the Kurchatov Institute.
Description.
According to this criterion a deterministic trajectory will begin to move
between two nonlinear resonances in a chaotic and unpredictable manner, 
in the parameter range
Here formula_2 is the perturbation parameter,
while 
formula_3
is the resonance-overlap parameter, given by the ratio of the
unperturbed resonance width in frequency
formula_4
(often computed in the pendulum
approximation and proportional to the square-root of perturbation),
and the frequency difference 
formula_5
between two unperturbed resonances. Since its introduction, the Chirikov criterion has become an important analytical tool for the determination of the chaos border.