Abstract

We study how the existence of a large orbit for a lifting of the map affects its set of periods. We mainly study the circle case, where a characterization is known. For this case we show that if the map has degree positive and has a large orbit then it has periodic points of all periods. We also give examples showing that this result does not hold when the degree is non positive. Finally we discuss what is known in the more difficult case of the sigma maps.

In Collaboration with: S. Ruette