Simon Baker

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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 $I ¨ : [0, \infty) \to (0, 1]$ satisfying $lim_{I^¾ \to \infty} I ¨ (I^¾) = 0$ , we prove the existence of i) self-similar measures and ii) nonlinear $C^{\infty}$ 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 $I^¼$ on $R^{d}$ under a large family of non-linear maps $F : R^{d} \to R$ exh…