Self-similarity in inverse limit spaces of the tent family

Barge, Marcy; Brucks, Karen; Diamond, Beverly

doi:10.1090/S0002-9939-96-03690-8

Self-similarity in inverse limit spaces of the tent family
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by Marcy Barge, Karen Brucks and Beverly Diamond

Proc. Amer. Math. Soc. 124 (1996), 3563-3570

DOI: https://doi.org/10.1090/S0002-9939-96-03690-8

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Abstract:

Taking inverse limits of the one-parameter family of tent maps of the interval generates a one-parameter family of inverse limit spaces. We prove that, for a dense set of parameters, these spaces are locally, at most points, the product of a Cantor set and an arc. On the other hand, we show that there is a dense $G_\delta$ set of parameters for which the corresponding space has the property that each neighborhood in the space contains homeomorphic copies of every inverse limit of a tent map.

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