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

 

Diffeomorphisms of the torus with wandering domains


Author: Patrick D. McSwiggen
Journal: Proc. Amer. Math. Soc. 117 (1993), 1175-1186
MSC: Primary 58F15; Secondary 58F13
MathSciNet review: 1154247
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Abstract: Examples of $ {C^{3 - \varepsilon }}$ diffeomorphisms of the $ 2$-torus are constructed, each of which is semiconjugate to an ergodic translation but has a wandering domain with dense orbit. This is a generalization of a classical example on the circle due to Denjoy.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1154247-6
PII: S 0002-9939(1993)1154247-6
Keywords: Toral diffeomorphism, Denjoy counterexamples, wandering domain
Article copyright: © Copyright 1993 American Mathematical Society