Inverse limits and full families

Authors

Jonathon E. Fassett, Central Washington University

Document Type

Article

Department or Administrative Unit

Mathematics

Publication Date

4-28-2004

Abstract

In this paper we investigate inverse limits on [0,1] using a single bonding map chosen from a Full family (one-parameter family of C¹ unimodal maps). Our investigation makes use of the renormalization operator utilized by Feigenbaum to explain the universal way in which Full families transition from simple to complicated dynamics. Among other results, we show that up through the Feigenbaum value the inverse limit is hereditarily decomposable with a fascinating pattern in the appearance of topological sin(1x)" role="presentation">-curves. Approaching the Feigenbaum value from above we see a similar pattern in the appearance of the Brouwer–Janiszewski–Knaster indecomposable continuum.

Comments

This article was originally published in Topology and its Applications. The full-text article from the publisher can be found here.

Due to copyright restrictions, this article is not available for free download from ScholarWorks @ CWU.

Recommended Citation

Fassett, J. E. (2004). Inverse limits and full families. Topology and Its Applications, 139(1–3), 237–252. https://doi.org/10.1016/j.topol.2003.11.002

Journal

Topology and Its Applications

Copyright

Copyright © 2003 Elsevier B.V. All rights reserved.