Subcontinua of inverse limit spaces of unimodal maps

Karen Brucks; Henk Bruin

Fundamenta Mathematicae (1999)

  • Volume: 160, Issue: 3, page 219-246
  • ISSN: 0016-2736

Abstract

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We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal maps as subcontinua.

How to cite

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Brucks, Karen, and Bruin, Henk. "Subcontinua of inverse limit spaces of unimodal maps." Fundamenta Mathematicae 160.3 (1999): 219-246. <http://eudml.org/doc/212390>.

@article{Brucks1999,
abstract = {We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal maps as subcontinua.},
author = {Brucks, Karen, Bruin, Henk},
journal = {Fundamenta Mathematicae},
keywords = {unimodal maps; inverse limit},
language = {eng},
number = {3},
pages = {219-246},
title = {Subcontinua of inverse limit spaces of unimodal maps},
url = {http://eudml.org/doc/212390},
volume = {160},
year = {1999},
}

TY - JOUR
AU - Brucks, Karen
AU - Bruin, Henk
TI - Subcontinua of inverse limit spaces of unimodal maps
JO - Fundamenta Mathematicae
PY - 1999
VL - 160
IS - 3
SP - 219
EP - 246
AB - We discuss the inverse limit spaces of unimodal interval maps as topological spaces. Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied. Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (non-trivial) subcontinua. Also, maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal maps as subcontinua.
LA - eng
KW - unimodal maps; inverse limit
UR - http://eudml.org/doc/212390
ER -

References

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