Chirikov Standard Map

The Chirikov standard map is an area preserving map of a cylinder or torus onto itself, governed by a single perturbation parameter, that models a simple mechanical rotator given periodic kicks and serves as one of the most studied examples of a Hamiltonian system capable of producing chaotic motion. It was introduced in 1969 by the Russian physicist Boris Chirikov as a way to study the transition from smooth, predictable orbits to chaotic ones as the strength of the kicking parameter increases. For small values of the parameter, most orbits remain confined to smooth invariant curves as described by the Kolmogorov-Arnold-Moser, or KAM, theorem, but as the parameter grows past a critical threshold these curves break apart and orbits can wander chaotically across large regions of the available space, a transition known as the onset of global chaos. Because of the clarity with which it demonstrates this transition, the standard map became a central testing ground for the broader theory of Hamiltonian chaos.