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Non-invertible planar self-affine sets
Published online by Cambridge University Press: 08 May 2024
Abstract
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.
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Cambridge Philosophical Society