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

 

A ``universal'' dynamical system generated by a continuous map of the interval


Authors: David Pokluda and Jaroslav Smítal
Journal: Proc. Amer. Math. Soc. 128 (2000), 3047-3056
MSC (1991): Primary 58F12, 58F08, 58F03, 26A18
Published electronically: March 3, 2000
MathSciNet review: 1712885
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Abstract:

In this paper we show that there is a continuous map $f:I\rightarrow I$of the interval such that any $\omega$-limit set $W$ of any continuous map $g:I\rightarrow I$ can be transformed by a homeomorphism $I\rightarrow I$ to an $\omega$-limit set $\tilde W$ of $f$. Consequently, any nowhere-dense compact set and any finite union of compact intervals is a homeomorphic copy of an $\omega$-limit set of $f$.


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Additional Information

David Pokluda
Affiliation: Institute of Mathematics, Silesian University, 746 01 Opava, Czech Republic
Email: David.Pokluda@fpf.slu.cz

Jaroslav Smítal
Affiliation: Institute of Mathematics, Silesian University, 746 01 Opava, Czech Republic
Email: smital@fpf.slu.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05679-3
PII: S 0002-9939(00)05679-3
Received by editor(s): November 1, 1998
Published electronically: March 3, 2000
Additional Notes: This research was supported, in part, by contract No. 201/97/0001 from the Grant Agency of the Czech Republic. Support of this institution is gratefully acknowledged.
Communicated by: Michael Handel
Article copyright: © Copyright 2000 American Mathematical Society