2 citations · 8 across the 16 of their papers we have counts for
5 papers · 1 filter
The dimension of projections of self-affine sets and measures
Kenneth Falconer, Tom Kempton
Let E be a plane self-affine set defined by affine transformations with linear parts given by matrices with positive entries. We show that if mu is a Bernoulli measure on E with di…
The random continued fraction transformation
Charlene Kalle, Tom Kempton, Evgeny Verbitskiy
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the Rényi (or backwards) continued fraction map. We…
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…
Planar self-affine sets with equal Hausdorff, box and affinity dimensions
Kenneth Falconer, Tom Kempton
Using methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-…
Bernoulli Convolutions and 1D Dynamics
Tom Kempton, Tomas Persson
We describe a family of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are p…