Rotation sets for orbits of degree one circle maps

Abstract Let F be the lifting of a circle map of degree one. In [?] a notion of F-rotation interval of a point x ∈ S1 was given. In this paper we define and study a new notion of a rotation set of a point which preserves more of the dynamical information contained in the sequences {Fn(y)}∞n=0 than the preserved by the one from [?]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [?] in our settings. 1 Introduction and statement of the main results Let C1(S1) be the class of all continuous maps of the circle into itself of degree one. Let f ∈ C1(S1) and let F: R − → R be a lifting of f. Denote by pi the canonical projection from R to S1. It is well known that, when f is a homeomorphism, then limn→ ∞ F n(y)−