Abstract
The dynamics of the circle map is studied in the supercritical regime where the map is not invertible and thus the trajectory elements are clustered on the circle. Existence of a simple ordering structure is established for trajectories with arbitrary irrational winding number. A previously developed formalism is then generalized to predict the trajectories when the winding number is quadratically irrational. Explicit results are given for a simple case.
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Sarkar, S.K. Supercritical ordered trajectories with quadratically irrational winding number. J Stat Phys 37, 385–405 (1984). https://doi.org/10.1007/BF01011840
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DOI: https://doi.org/10.1007/BF01011840