Fourier transform and expanding maps on Cantor sets

Tuomas Sahlsten, Connor Stevens

Published 2020-09-03Version 1

We study the Fourier transforms $\widehat{\mu}(\xi)$ of Gibbs measures $\mu$ for uniformly expanding maps $T$ of bounded distortions on Cantor sets with strong separation condition. When $T$ is totally non-linear and Hausdorff dimension of $\mu$ is large enough, then $\widehat{\mu}(\xi)$ decays at a polynomial rate as $|\xi| \to \infty$.