### *Cancelled* A dimension gap between self-affine measures and self-affine sets.

Ergodic Theory and Dynamical Systems Seminar

14th March 2019, 2:00 pm – 3:00 pm

Howard House, 4th Floor Seminar Room

*Cancelled* A classical theorem of J.E. Hutchinson states that every self-similar set satisfying the open set condition admits a self-similar measure with Hausdorff dimension equal to the similarity dimension. I will describe a result which shows that the analogue of this statement for self-affine sets and self-affine measures is false under a generically-satisfied algebraic condition on the linear parts of the affinities. This is a work in progress with Çağrı Sert.

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