92 citations · 502 across the 56 of their papers we have counts for
5 papers · 1 filter
Structure of distributions generated by the scenery flow
Antti Käenmäki, Tuomas Sahlsten, Pablo Shmerkin
We expand the ergodic theory developed by Furstenberg and Hochman on dynamical systems that are obtained from magnifications of measures. We prove that any fractal distribution in…
Non-conformal repellers and the continuity of pressure for matrix cocycles
De-Jun Feng, Pablo Shmerkin
The pressure function plays a fundamental role in the calculation of the dimension of "typical" self-affine sets, where is the family of linear mapp…
Self-affine sets and the continuity of subadditive pressure
Pablo Shmerkin
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…
On the exceptional set for absolute continuity of Bernoulli convolutions
Pablo Shmerkin
We prove that the set of exceptional such that the associated Bernoulli convolution is singular has zero Hausdorff dimension, and likewise for biased Bernoulli convo…
Equidistribution from Fractals
Michael Hochman, Pablo Shmerkin
We give a fractal-geometric condition for a measure on [0,1] to be supported on points x that are normal in base n, i.e. such that the sequence x,nx,n^2 x,... equidistributes modul…