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. © Springer-Verlag Berlin Heidelberg 2014.
CITATION STYLE
Shmerkin, P. (2014). Self-affine Sets and the Continuity of Subadditive Pressure. In Springer Proceedings in Mathematics and Statistics (Vol. 88, pp. 325–342). Springer New York LLC. https://doi.org/10.1007/978-3-662-43920-3_12
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