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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A $C^1$ function for which the $\omega$-limit points are not contained in the closure of the periodic points


Authors: Emma D'Aniello and T. H. Steele
Journal: Trans. Amer. Math. Soc. 355 (2003), 2545-2556
MSC (2000): Primary 26A18; Secondary 54H20
Published electronically: February 4, 2003
MathSciNet review: 1974002
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Abstract: We develop a $C^1$ function $f: [- \frac{1}{6}, 1] \rightarrow [- \frac{1}{6}, 1]$ for which $\Lambda(f) \not= \overline{P(f)}$. This answers a query from Block and Coppel (1992).


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Additional Information

Emma D'Aniello
Affiliation: Dipartimento di Matematica, Seconda Università degli Studi di Napoli, Via Vivaldi 43, 81100 Caserta, Italia
Email: emma.daniello@unina2.it

T. H. Steele
Affiliation: Department of Mathematics, Weber State University, Ogden, Utah 84408-1702
Email: thsteele@weber.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03258-6
PII: S 0002-9947(03)03258-6
Received by editor(s): May 20, 2002
Received by editor(s) in revised form: August 13, 2002
Published electronically: February 4, 2003
Article copyright: © Copyright 2003 American Mathematical Society