Paper of Ian Morris appears in the Transactions of the American Mathematical Society

The paper “On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems” co-authored by Ian Morris and Pablo Shmerkin (Universidad Torcuato di Tella, Argentina) has been published in the Transactions of the American Mathematical Society. In the paper they show that the affinity dimension of a planar self-affine set is equal to the supremum of the Lyapunov dimensions of self-affine measures supported on self-affine proper subsets of the original set. The paper is available electronically here. The main result of this article was applied by Bárány, Hochman and Rapaport in their paper “Hausdorff dimension of planar self-affine sets and measures” (to appear in Inventiones Mathematicae) as part of their solution to the dimension problem for planar self-affine sets. Pablo is a former Research Fellow and Lecturer at the University of Surrey.