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On the magnification of Cantor sets and their limit models. (English) Zbl 0843.28002

The authors show that cookie-cutter sets \(C\) have well defined limit models for their infinitesimal geometry. It turns out that diffeomorphic copies of \(C\) have the same limit models. To prove this they introduce magnifications around translations of points as topological flows on the hyperspace of closed non-empty sets in the line equipped with the Fell topology. They also point out the relation with Sullivan’s scaling function and to the definition of fractal sets as given by Wicks.

MSC:

28A80 Fractals
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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References:

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