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.
[pdf (published paper)]