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arXiv · 1309.4730

Self-affine sets and the continuity of subadditive pressure

Pablo Shmerkin
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Abstract

The affinity dimension is a number associated to an iterated function system of affine maps, which is fundamental in the study of the fractal dimensions of self-affine sets. De-Jun Feng and the author recently solved a folklore open problem, by proving that the affinity dimension is a continuous function of the defining maps. The proof also yields the continuity of a topological pressure arising in the study of random matrix products. I survey the definition, motivation and main properties of the affinity dimension and the associated SVF topological pressure, and give a proof of their continuity in the special case of ambient dimension two.

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Pablo Shmerkin. 2013-09-18. Self-affine sets and the continuity of subadditive pressure. https://arxiv.org/abs/1309.4730

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