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

 

$C^n$ interval maps not Borel conjugate to any $C^{\infty}$ map


Author: Sylvie Ruette
Journal: Proc. Amer. Math. Soc. 132 (2004), 1091-1093
MSC (2000): Primary 37E05, 37C15; Secondary 37A05
Published electronically: August 20, 2003
MathSciNet review: 2045425
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Abstract: We show that there exist interval maps that are not Borel conjugate to any $C^{\infty}$ map. These examples can be chosen to be topologically mixing and $C^n$, for any finite, arbitrarily large $n$.


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Additional Information

Sylvie Ruette
Affiliation: Universitat Autònoma de Barcelona– Departament de Matemàtiques– Edifici Cc–08193 Cerdanyola del Vallès–Barcelona–Spain
Address at time of publication: Laboratoire de Mathématiques, Topologie et Dynamique, Université Paris Sud, 91405 Orsay, France
Email: ruette@mat.uab.es, sylvie.ruette@math.u-psud.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07222-8
PII: S 0002-9939(03)07222-8
Received by editor(s): November 28, 2002
Published electronically: August 20, 2003
Communicated by: Michael Handel
Article copyright: © Copyright 2003 American Mathematical Society