2 citations · 4 across the 6 of their papers we have counts for
7 papers
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…
Intermediate dimensions
Kenneth J. Falconer, Jonathan M. Fraser, Tom Kempton
We introduce a continuum of dimensions which are `intermediate' between the familiar Hausdorff and box dimensions. This is done by restricting the families of allowable covers in t…
On the Hausdorff Dimension of Bernoulli Convolutions
Shigeki Akiyama, De-Jun Feng, Tom Kempton +1
We give an expression for the Garsia entropy of Bernoulli convolutions in terms of products of matrices. This gives an explicit rate of convergence of the Garsia entropy and shows…
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…