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Denjoy minimal sets are far from affine

Published online by Cambridge University Press:  21 November 2002

ALEC NORTON KERCHEVAL
ALEC NORTON KERCHEVAL
Affiliation:
Department of Mathematics, Florida state University, Tallahassee, FL 32306, USA (e-mail: kercheval@math.fsu.edu)
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Abstract

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Not every Cantor set can arise as the minimal set for a C^1 diffeomorphism of the circle. For example, McDuff has shown that the usual ‘middle thirds’ Cantor set cannot arise in this way. In this paper we exclude a suitable neighborhood of the class of affine Cantor sets.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 22 , Issue 6 , December 2002, pp. 1803 - 1812
Copyright
2002 Cambridge University Press