6 citations · 7 across the 7 of their papers we have counts for
7 papers
Pair correlation statistics for dynamical systems
Simon Baker, Mike Todd
We study the pair correlation statistics of orbits generated by maps on the interval. We show that under suitable mixing and multifractal assumptions, the pair correlation statisti…
Self-similar and self-conformal measures with slow Fourier decay
Simon Baker, Amlan Banaji
Given any function satisfying , we prove the existence of i) self-similar measures and ii) nonlinear self-conf…
Distinct dimensions for attractors of bi-Lipschitz iterated function systems
Simon Baker, Amlan Banaji, De-Jun Feng +2
In this paper, we construct an iterated function system on the line consisting of two bi-Lipschitz contractions whose attractor has distinct lower, Hausdorff, lower box, upper box,…
On the strong separation condition for self-similar iterated function systems with random translations
Simon Baker, Derong Kong, Zhiqiang Wang
Given a self-similar iterated function system acting on , we can generate a parameterised family of iterated function systems b…
Polynomial Fourier decay for fractal measures and their pushforwards
Simon Baker, Amlan Banaji
We prove that the pushforwards of a very general class of fractal measures on under a large family of non-linear maps exhi…
On the complexity of the set of codings for self-similar sets and a variation on the construction of Champernowne
Simon Baker, Derong Kong
Let be a collection of points in The set naturally gives rise to a family of iterated function systems consisting of co…
Induced Random -transformation
Simon Baker, Karma Dajani
In this article we study the first return map defined on the switch region induced by the greedy and lazy maps. In particular we study the allowable sequences of return times, and…