Non-invertible planar self-affine sets

We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and differ when they are small. Our study relies on thermodynamic f...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 2024-07, Vol.177 (1), p.49-65
Main Authors: KÄENMÄKI, ANTTI, NISSINEN, PETTERI
Format: Article
Language:English
Subjects:
Eigenvalues
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Summary:We compare the dimension of a non-invertible self-affine set to the dimension of the respective invertible self-affine set. In particular, for generic planar self-affine sets, we show that the dimensions coincide when they are large and differ when they are small. Our study relies on thermodynamic formalism where, for dominated and irreducible matrices, we completely characterise the behaviour of the pressures.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004124000136