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Hofbauer towers and inverse limit spaces


Author: Lori Alvin
Journal: Proc. Amer. Math. Soc. 141 (2013), 4039-4048
MSC (2010): Primary 54H20, 37B45; Secondary 37E05
DOI: https://doi.org/10.1090/S0002-9939-2013-11667-9
Published electronically: July 18, 2013
MathSciNet review: 3091795
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Abstract: In this paper we use Hofbauer towers for unimodal maps to study the collection of endpoints of the associated inverse limit spaces. It is shown that if $ f$ is a unimodal map for which the kneading map $ Q_f(k)$ tends to infinity and $ f\vert _{\omega (c)}$ is one-to-one, then the collection of endpoints of $ (I,f)$ is precisely the set $ \mathcal {E}_f = \{( x_0,x_1,\ldots ) \in (I,f) \mid x_i\in \omega (c)$ for all $ i\in \mathbb{N}\}$.


References [Enhancements On Off] (What's this?)

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Additional Information

Lori Alvin
Affiliation: Department of Mathematics and Statistics, University of West Florida, 11000 University Parkway, Pensacola, Florida 32514
Email: lalvin@uwf.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11667-9
Keywords: Hofbauer tower, inverse limit spaces, kneading maps, endpoints
Received by editor(s): October 19, 2011
Received by editor(s) in revised form: January 23, 2012
Published electronically: July 18, 2013
Communicated by: Bryna Kra
Article copyright: © Copyright 2013 American Mathematical Society

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