Cyclic approximation of irrational rotations

Author:
A. Iwanik

Journal:
Proc. Amer. Math. Soc. **121** (1994), 691-695

MSC:
Primary 28D05; Secondary 58F11

MathSciNet review:
1221724

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Abstract: We prove that an irrational number admits a rational approximation iff the irrational rotation admits cyclic approximation with speed . As an application to earlier results we obtain that a generic Anzai skew product over every irrational rotation is rank-1 and for a.e. most skew products admit cyclic approximation with speed .

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1994-1221724-X

Article copyright:
© Copyright 1994
American Mathematical Society