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Scaling distances on finitely ramified fractals.
- Source :
-
Kyoto Journal of Mathematics . 2017, Vol. 57 Issue 3, p475-504. 30p. - Publication Year :
- 2017
-
Abstract
- In this article we study two problems about the existence of a distance d on a given fractal having certain properties. In the first problem, we require that the maps ψi defining the fractal be Lipschitz of prescribed constants less than 1 with respect to the distance d, and in the second one, we require that arbitrary compositions of the maps ψi be uniformly bi-Lipschitz of related constants. Both problems have been investigated previously by other authors. In this article, on a large class of finitely ramified fractals,we prove that these two problems are equivalent and give a necessary and sufficient condition for the existence of such a distance. Such a condition is expressed in terms of asymptotic behavior of the product of certain matrices associated to the fractal. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 21562261
- Volume :
- 57
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Kyoto Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 124320071
- Full Text :
- https://doi.org/10.1215/21562261-2017-0003