On the symmetry lines of the standard mapping. (English) Zbl 0612.58023
The Taylor and Chirikov standard mapping is used as a model to represent the dynamics of non-integrable systems by means of the Poincaré section of the trajectories intersecting a fixed plane of the phase space. This study is based on a systematic use of the decomposition of the standard mapping in a product of two involutions, forming a group including the iterates of the mapping and their inverses. The symmetry lines of the family of involutions determine the position of the periodic points and explain the onset of new chains of periodic points produced by the winding of the symmetry lines around the stable periodic points.
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