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Tuesday 07 Jun 2022Lyapunov dimension and self-affine sets

Thomas Jordan - University of Bristol

LSI Seminar Room B 13:30-14:30

We will introduce self-affine measures and the notion of Lyapunov dimension and show that the Hausdorff dimension of self-affine sets is always bounded above by the Lyapunov dimension. We will then show a family of examples under which it is possible to give a precise condition for when the two dimensions are equal. We will then look at an extension to ergodic measures and show how work on the dimension of ergodic measures on self-similar sets can give new results on dimension for measures on self-affine set. This talk contains joint work with Ariel Rapaport and also with Jonathan Fraser and Natalia Jurga.

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