Abstract
A piecewise linear map with one discontinuity is studied by analytic means in the two-dimensional parameter space. When the slope of the map is less than unity, periodic orbits are present, and we give the precise symbolic dynamic classification of these. The localization of the periodic domains in parameter space is given by closed expressions. The winding number forms a devil's terrace, a two-dimensional function whose cross sections are complete devils's staircases. In such a cross section the complementary set to the periodic intervals is a Cantor set with dimensionD=0.
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Ding, E.J., Hemmer, P.C. Exact treatment of mode locking for a piecewise linear map. J Stat Phys 46, 99–110 (1987). https://doi.org/10.1007/BF01010333
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DOI: https://doi.org/10.1007/BF01010333