Rotation sets for orbits of degree one circle maps

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Abstract

Let F be the lifting of a circle map of degree one. In [Bamón et al., 1984] 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 one preserved from [Bamón et al., 1984]. In particular, we characterize dynamically the endpoints of these sets and we obtain an analogous version of the Main Theorem of [Bamón et al., 1984] in our settings.
Original languageEnglish
Pages (from-to)429-437
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume12
DOIs
Publication statusPublished - 1 Jan 2002

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