Self-affine sets and the continuity of subadditive pressure
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2013
- DOI:
- 10.48550/arXiv.1309.4730
- arXiv:
- arXiv:1309.4730
- Bibcode:
- 2013arXiv1309.4730S
- Keywords:
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- Mathematics - Dynamical Systems;
- Primary 37C45;
- 37D35;
- 37H15
- E-Print:
- 15 pages, no figures