A “universal” dynamical system generated by a continuous map of the interval
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- by David Pokluda and Jaroslav Smítal PDF
- Proc. Amer. Math. Soc. 128 (2000), 3047-3056 Request permission
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 $f$.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3047-3056
- MSC (1991): Primary 58F12, 58F08, 58F03, 26A18
- DOI: https://doi.org/10.1090/S0002-9939-00-05679-3
- MathSciNet review: 1712885