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Commuting endomorphisms of the circle

Published online by Cambridge University Press:  19 September 2008

Aimee S. A. Johnson  and
Daniel J. Rudolph
Aimee S. A. Johnson
Affiliation:
Mathematics Department, Tufts University, Medford, MA 02155, USA
Daniel J. Rudolph
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA
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Abstract

In this paper the results of Shub and Sacksteder are extended to the following theorem: let ƒ1 and ƒ2 be two commuting, expansive, orientation-preserving maps of the circle with a common fixed point and with both in C1+ε or Cr, r ≥2. Assume ƒ1 is p-to-1 and ƒ2 is q-to-1 where p and q generate a nonlacunary semigroup. Then there exists a diffeomorphism g of the same class such that gƒ1g−1 = TP and gƒ2g−1 = Tq.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 4 , December 1992 , pp. 743 - 748
Copyright
Copyright © Cambridge University Press 1992

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References

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