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

DOI:
https://doi.org/10.1090/S0002-9939-00-05679-3

Published electronically:
March 3, 2000

MathSciNet review:
1712885

Full-text PDF

Abstract | References | Similar Articles | Additional Information

In this paper we show that there is a continuous map of the interval such that any -limit set of any continuous map can be transformed by a homeomorphism to an -limit set of . Consequently, any nowhere-dense compact set and any finite union of compact intervals is a homeomorphic copy of an -limit set of .

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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:
https://doi.org/10.1090/S0002-9939-00-05679-3

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