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Rotation Sets for orbits of Degree One Circle Maps

Let F be the lifting of a circle map of degree one. In [Bamon et al., 1984] a notion of F-rotation interval of a point was given. In this paper we define and study a new notion of a rotation set of point which preserves more of the dynamical information contained in the sequences than the one preserved from [Bamon et al., 1984]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [Bamon et al., 1984] in our settings.