Dimension and measures on sub-self-affine sets

We show that in a typical sub-self-affine set, the Hausdorff and the Minkowski dimensions coincide and equal the zero of an appropriate topological pressure. This gives a partial positive answer to the question of Falconer. We also study the properties of the topological pressure and the existence a...

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Bibliographic Details
Published in:arXiv.org 2017-01
Main Authors: Käenmäki, Antti, Vilppolainen, Markku
Format: Article
Language:English
Subjects:
Topology
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Summary:We show that in a typical sub-self-affine set, the Hausdorff and the Minkowski dimensions coincide and equal the zero of an appropriate topological pressure. This gives a partial positive answer to the question of Falconer. We also study the properties of the topological pressure and the existence and the uniqueness of natural measures supported on a sub-self-affine set.
ISSN:2331-8422
DOI:10.48550/arxiv.1701.08611