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

Author(s): Víctor Jiménez López; L'ubomír Snoha
Journal: Proc. Amer. Math. Soc. 125 (1997), 1667-1673.
MSC (1991): Primary 26A18; Secondary 58F08, 54H20
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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
Email: vjimenez@fcu.um.es

L'ubomír Snoha
Affiliation: Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Tajovsk\ee ho 40, 974 01 Bansk\aaa Bystrica, Slovakia
Email: snoha@bb.sanet.sk

DOI: 10.1090/S0002-9939-97-03452-7
PII: S 0002-9939(97)03452-7
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
Copyright of article: Copyright 1997, American Mathematical Society

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J. Hu and C. Tresser , Period doubling, entropy, and renormalization, Fund. Math. 155 (1998), 237--249.

R. Hric, Chaos and topological entropy in one-dimensional dynamics, Ph. D. Thesis, Comenius University, Bratislava, 1998.

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