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Denjoy's theorem with exponents

Author: Alec Norton
Journal: Proc. Amer. Math. Soc. 127 (1999), 3111-3118
MSC (1991): Primary 58F03; Secondary 28A80
Published electronically: April 23, 1999
MathSciNet review: 1600129
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Abstract | References | Similar Articles | Additional Information

Abstract: If $X$ is the (unique) minimal set for a $C^{1+\alpha }$ diffeomorphism of the circle without periodic orbits, $0<\alpha <1$, then the upper box dimension of $X$ is at least $\alpha$. The method of proof is to introduce the exponent $\alpha $ into the proof of Denjoy's theorem.

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Additional Information

Alec Norton
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712

Keywords: Box dimension, minimal sets, Cantor sets, circle diffeomorphisms
Received by editor(s): July 23, 1997
Received by editor(s) in revised form: December 15, 1997
Published electronically: April 23, 1999
Communicated by: Mary Rees
Article copyright: © Copyright 1999 American Mathematical Society