92 citations · 502 across the 56 of their papers we have counts for
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math.DS2016
On Furstenberg's intersection conjecture, self-similar measures, and the norms of convolutions
Pablo Shmerkin
We study a class of measures on the real line with a kind of self-similar structure, which we call dynamically driven self-similar measures, and contain proper self-similar measure…
math.DS2016
On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems
Ian D. Morris, Pablo Shmerkin
Under mild conditions we 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-…