2 citations · 4 across the 9 of their papers we have counts for
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Local dimension spectrum for dominated planar self-affine sets
Alex Batsis, Antti Käenmäki, Tom Kempton
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this…
Towards Absolutely Continuous Bernoulli Convolutions
Alex Batsis, Tom Kempton
We show how to turn the question of the absolute continuity of Bernoulli convolutions into one of counting the growth of the number of overlaps in the system. When the contraction…
Measures on the Spectra of Algebraic Integers
Tom Kempton, Alex Batsis
Given a real number beta > 1, the spectrum of beta is a well studied dynamical object. In this article we show the existence of a certain measure on the spectrum of beta related to…
The Scenery Flow for Self-Affine Measures
Tom Kempton
We describe the scaling scenery associated to Bernoulli measures supported on separated self-affine sets under the condition that certain projections of the measure are absolutely…
On the Invariant Density of the Random Beta-Transformation
Tom Kempton
We construct a Lebesgue measure preserving natural extension of the random beta-transformation. This allows us to give a formula for the density of the absolutely continuous invari…
Digit Frequencies and Bernoulli Convolutions
Tom Kempton
It is well known that the Bernoulli convolution associated to the golden mean has Hausdorff dimension less than 1, i.e. that there exists a set with and $dim_H…