4 papers
math.DS2026
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…
math.DS2026
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-…
math.DS2025
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,…
math.DS2025
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 exh…