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Diffeomorphisms of the k-torus with wandering domains

Published online by Cambridge University Press:  14 October 2010

Patrick D. McSwiggen
Patrick D. McSwiggen
Affiliation:
Department of Mathematical Sciences, The University of Cincinnati, Cincinnati OH 45221–0025, USA
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Abstract

It is shown that diffeomorphisms analogous to a classical example on the circle due to Denjoy can be constructed on the general k-torus. Such a diffeomorphism has the property that it is semiconjugate to an ergodic translation but has a wandering domain with dense orbit. The construction on the k-torus can be made Cr, and by a Cr small perturbation of a translation, for any r < k + 1.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 6 , December 1995 , pp. 1189 - 1205
Copyright
Copyright © Cambridge University Press 1995

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References

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