 Chirikov criterion

The Chirikov criterion or Chirikov resonanceoverlap criterion was established by the Russian physicist Boris Chirikov. Back in 1959, he published a seminal article (Atom. Energ. 6: 630 (1959)), 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. As in an old oriental tale, Boris Chirikov opened such a bottle, and freed the genie of chaos, which spread the world over.
Contents
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 K is the perturbation parameter, while S = Δω_{r} / Δ_{d} is the resonanceoverlap parameter, given by the ratio of the unperturbed resonance width in frequency Δω_{r} (often computed in the pendulum approximation and proportional to the squareroot of perturbation), and the frequency difference Δ_{d} between two unperturbed resonances. Since its introduction, the Chirikov criterion has become an important analytical tool for the determination of the chaos border.
See also
 Chirikov criterion at Scholarpedia
 Chirikov standard map and standard map
 Boris Chirikov and Boris Chirikov at Scholarpedia
References
 B.V.Chirikov, "Resonance processes in magnetic traps", At. Energ. 6: 630 (1959) (in Russian [1])(Engl. Transl., J. Nucl. Energy Part C: Plasma Phys. 1: 253 (1960)[2])
 B.V.Chirikov, "Research concerning the theory of nonlinear resonance and stochasticity", Preprint N 267, Institute of Nuclear Physics, Novosibirsk (1969), (Engl. Trans., CERN Trans. 7140 (1971))
 B.V.Chirikov, "A universal instability of manydimensional oscillator systems", Phys. Rep. 52: 263 (1979)
 A.J.Lichtenberg and M.A.Lieberman (1992). Regular and Chaotic Dynamics. Springer, Berlin. ISBN 9780387977454. Springer link
External links
 website dedicated to Boris Chirikov
 Special Volume dedicated to 70th of Boris Chirikov: Physica D 131:14 vii (1999) and arXiv
Categories: Chaos theory
 Chaotic maps
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