Periodic orbits of large diameter for circle maps

Proceedings of the American Mathematical Society, 138, No 9, 3211-3217, 2010.


Let f be a continuous circle map and let F be a lifting of f. In this note we study how the existence of a large orbit for F affects its set of periods. More precisely, we show that, if F is of positive degree and has a periodic orbit of diameter larger than 1, then F has periodic points of period n for all positive integers, and thus so has f. We also give examples showing that this result does not hold when the degree is non positive.

Paper: [arXiv:1901.01533] [pdf (published paper)]