Self-similarity in inverse limit spaces of the tent family. (English) Zbl 0917.54041
Summary: Taking inverse limits of the one-parameter family of tent maps of the interval generates a one-parameter family of inverse limit spaces. The authors 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, they 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.
MSC:
| 54F15 | Continua and generalizations |
| 37C70 | Attractors and repellers of smooth dynamical systems and their topological structure |
| 37E99 | Low-dimensional dynamical systems |
| 54H20 | Topological dynamics (MSC2010) |
References:
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