Hofbauer towers and inverse limit spaces

Alvin, Lori

doi:10.1090/S0002-9939-2013-11667-9

Hofbauer towers and inverse limit spaces
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Proc. Amer. Math. Soc. 141 (2013), 4039-4048 Request permission

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 $f|_{\omega (c)}$ 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 $i\in \mathbb {N}\}$.

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