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The standard map (also known as the Chirikov–Taylor map or as the Chirikov standard map) is an area-preserving chaotic map from a square with side onto itself.〔 It is constructed by a Poincaré's surface of section of the kicked rotator, and is defined by: : : where and are taken modulo . The properties of chaos of the standard map were established by Boris Chirikov in 1969. See more details at (Scholarpedia entry ). ==Physical model== This map describes the Poincaré's surface of section of the motion of a simple mechanical system known as the kicked rotator. The kicked rotator consists of a stick that is free of the gravitational force, which can rotate frictionlessly in a plane around an axis located in one of its tips, and which is periodically kicked on the other tip. The standard map is a surface of section applied by a stroboscopic projection on the variables of the kicked rotator.〔 The variables and respectively determine the angular position of the stick and its angular momentum after the ''n''-th kick. The constant ''K'' measures the intensity of the kicks on the kicked rotator. The kicked rotator approximates systems studied in the fields of mechanics of particles, accelerator physics, plasma physics, and solid state physics. For example, circular particle accelerators accelerate particles by applying periodic kicks, as they circulate in the beam tube. Thus, the structure of the beam can be approximated by the kicked rotor. However, this map is interesting from a fundamental point of view in physics and mathematics because it is a very simple model of a conservative system that displays Hamiltonian chaos. It is therefore useful to study the development of chaos in this kind of system. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「standard map」の詳細全文を読む スポンサード リンク
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