All maps of type 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

DOI:
https://doi.org/10.1090/S0002-9939-97-03452-7

MathSciNet review:
1342034

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a continuous map of an interval into itself having periodic points of period for all and no other periods. It is shown that every neighborhood of contains a map such that the set of periods of the periodic points of 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:
https://doi.org/10.1090/S0002-9939-97-03452-7

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

Article copyright:
© Copyright 1997
American Mathematical Society