Self-similarity in inverse limit spaces of the tent family |
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Authors: | Marcy Barge Karen Brucks Beverly Diamond |
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Affiliation: | Department of Mathematics, Montana State University, Bozeman, Montana 59717 ; Department of Mathematical Sciences, University of Wisconsin at Milwaukee, Milwaukee, Wisconsin 53201 ; Department of Mathematics, University of Charleston, Charleston, South Carolina 29424 |
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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 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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