# Composants of the horseshoe

Fundamenta Mathematicae (1994)

- Volume: 144, Issue: 3, page 231-241
- ISSN: 0016-2736

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topBandt, Christoph. "Composants of the horseshoe." Fundamenta Mathematicae 144.3 (1994): 231-241. <http://eudml.org/doc/212026>.

@article{Bandt1994,

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.},

author = {Bandt, Christoph},

journal = {Fundamenta Mathematicae},

keywords = {horseshoe; bucket handle continuum; tent map},

language = {eng},

number = {3},

pages = {231-241},

title = {Composants of the horseshoe},

url = {http://eudml.org/doc/212026},

volume = {144},

year = {1994},

}

TY - JOUR

AU - Bandt, Christoph

TI - Composants of the horseshoe

JO - Fundamenta Mathematicae

PY - 1994

VL - 144

IS - 3

SP - 231

EP - 241

AB - 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.

LA - eng

KW - horseshoe; bucket handle continuum; tent map

UR - http://eudml.org/doc/212026

ER -

## References

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