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The speed interval: a rotation algorithm for endomorphisms of the circle

Published online by Cambridge University Press:  19 September 2008

Jan Barkmeijer
Jan Barkmeijer
Affiliation:
Mathematisch Instituut, Postbus 800, 9700 AV Groningen, The Netherlands
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Abstract

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Let f be a continuous map of the circle into itself of degree one. We introduce the notion of rotation algorithms. One of these algorithms associates each z ∈ S1 with an interval, the so-called speed interval S(z, f), which is contained in the rotation interval ρ(f) of f. In contrast with the rotation set ρ(z, f), the interval S(z, f) sometimes allows us to ascertain that ρ(f) is non-degenerate, by using only finitely many elements of {fn (z) | n ≥ 0}. We further show that all choices for ρ(z, f) and S(z, f) occur, for certain z ∈ S1 provided that ρ(z, f) ⊂ S(z, f) ⊂ ρ(f).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 1 , March 1988 , pp. 17 - 33
Copyright
Copyright © Cambridge University Press 1988

References

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