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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A pseudorotation with quadratic irrational rotation number


Author: Mark Turpin
Journal: Proc. Amer. Math. Soc. 140 (2012), 227-233
MSC (2010): Primary 37-XX; Secondary 11-XX, 26-XX, 54-XX, 58-XX
Published electronically: May 11, 2011
MathSciNet review: 2833535
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Abstract: We show, by explicit construction, that for any quadratic irrational number $ \alpha $, there exists a pseudorotation on an indecomposable cofrontier $ \Lambda $ with $ \alpha $ as its rotation number. Our construction builds on a family of examples of Brechner, Guay, and Mayer. They observe that in the pseudorotations they construct, irrational numbers of constant type are not realized as rotation numbers. Circle rotations can realize any rotation number, but this is to our knowledge the first example of a pseudorotation with a quadratic irrational rotation number, and hence an irrational of constant type.


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Additional Information

Mark Turpin
Affiliation: Department of Mathematics, University of Hartford, West Hartford, Connecticut 06117

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10886-4
PII: S 0002-9939(2011)10886-4
Received by editor(s): October 18, 2010
Received by editor(s) in revised form: October 30, 2010, and November 5, 2010
Published electronically: May 11, 2011
Communicated by: Bryna Kra
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.