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ArticleOriginal scientific text

Title

Composants of the horseshoe

Authors 1

Affiliations

  1. FR Mathematik/Informatik, Arndt-Universität, 17487 Greifswald, Germany

Abstract

The horseshoe or bucket handle continuum, defined as the inverse limit of the tent map, is one of the standard examples in continua theory as well as in dynamical systems. It is not arcwise connected. Its arcwise components coincide with composants, and with unstable manifolds in the dynamical setting. Knaster asked whether these composants are all homeomorphic, with the obvious exception of the zero composant. Partial results were obtained by Bellamy (1979), Dębski and Tymchatyn (1987), and Aarts and Fokkink (1991). We answer Knaster's question in the affirmative. The main tool is a very simple type of symbolic dynamics for the horseshoe and related continua.

Bibliography

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm144/fm14433.pdf

Fundamenta Mathematicae
1994/144/3
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Pages:
231-241
Main language of publication
English
Received
1993-02-02
Accepted
1993-08-25
Published
1994
Exact and natural sciences