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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$C^n$ interval maps not Borel conjugate to any $C^{\infty }$ map
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by Sylvie Ruette PDF
Proc. Amer. Math. Soc. 132 (2004), 1091-1093 Request permission

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 $n$.
References
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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
  • Received by editor(s): November 28, 2002
  • Published electronically: August 20, 2003
  • Communicated by: Michael Handel
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 1091-1093
  • MSC (2000): Primary 37E05, 37C15; Secondary 37A05
  • DOI: https://doi.org/10.1090/S0002-9939-03-07222-8
  • MathSciNet review: 2045425