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All maps of type $2^{\infty }$ are boundary maps

Authors: Víctor Jiménez López and L'ubomír Snoha
Journal: Proc. Amer. Math. Soc. 125 (1997), 1667-1673
MSC (1991): Primary 26A18; Secondary 58F08, 54H20
MathSciNet review: 1342034
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Abstract: Let $f$ be a continuous map of an interval into itself having periodic points of period $2^{n}$ for all $n\geq 0$ and no other periods. It is shown that every neighborhood of $f$ contains a map $g$ such that the set of periods of the periodic points of $g$ is finite. This answers a question posed by L. S. Block and W. A. Coppel.

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Additional Information

Víctor Jiménez López
Affiliation: Departamento de Matemá ticas, Universidad de Murcia, Campus de Espinardo, Aptdo. de Correos 4021, 30100 Murcia, Spain

L'ubomír Snoha
Affiliation: Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\ee ho 40, 974 01 Bansk\aaa Bystrica, Slovakia

Keywords: Map of type $2^{\infty }$, periodic point, solenoid
Received by editor(s): February 27, 1995
Received by editor(s) in revised form: May 2, 1995
Additional Notes: Most of the work on this paper was done during the stay of the first author at the Matej Bel University. The invitation and the support of this institution is gratefully acknowledged. The first author has been partially supported by the DGICYT PB91-0575 and the second author by the Slovak grant agency, grant number 1/1470/94.
Communicated by: Mary Rees
Article copyright: © Copyright 1997 American Mathematical Society