Subcontinua of inverse limit spaces of unimodal maps

Volume 160 / 1999

Karen Brucks, Henk Bruin Fundamenta Mathematicae 160 (1999), 219-246 DOI: 10.4064/fm-160-3-219-246

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.

Authors

  • Karen Brucks
  • Henk Bruin

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