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

Author(s): Sylvie Ruette
Journal: Proc. Amer. Math. Soc. 132 (2004), 1091-1093.
MSC (2000): Primary 37E05, 37C15; Secondary 37A05
Posted: August 20, 2003
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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: 10.1090/S0002-9939-03-07222-8
PII: S 0002-9939(03)07222-8
Received by editor(s): November 28, 2002.
Posted: August 20, 2003
Communicated by: Michael Handel
Copyright of article: Copyright 2003, American Mathematical Society

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