Genericity of dimension drop on self-affine sets

We prove that generically, for a self-affine set in Rd, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.

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Bibliographic Details
Published in:Statistics & probability letters 2017-07, Vol.126, p.18-25
Main Authors: Käenmäki, Antti, Li, Bing
Format: Article
Language:English
Subjects:
Products of matrices
Self-affine set
Singular value function
Thermodynamic formalism
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Summary:We prove that generically, for a self-affine set in Rd, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2017.02.028