Primary cycles on the circle

Block, Louis; Coven, Ethan M.; Jonker, Leo; Misiurewicz, Michał

doi:10.1090/S0002-9947-1989-0974779-4

Primary cycles on the circle
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by Louis Block, Ethan M. Coven, Leo Jonker and Michał Misiurewicz

Trans. Amer. Math. Soc. 311 (1989), 323-335

DOI: https://doi.org/10.1090/S0002-9947-1989-0974779-4

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Abstract:

We consider cycles, i.e., periodic orbits, of continuous degree one maps of the circle. One cycle forces another if every such map that has a cycle which looks like the first also has a cycle which looks like the second. We characterize primary cycles, i.e., those which force no other cycle of the same period.

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