Logarithmic Fourier decay for self conformal measures
Dynamical Systems
2022-03-04 v2 Classical Analysis and ODEs
Abstract
We prove that the Fourier transform of a self conformal measure on decays to at infinity at a logarithmic rate, unless the following holds: The underlying IFS is smoothly conjugated to an IFS that both acts linearly on its attractor and contracts by scales that are not Diophantine. Our key technical result is an effective version of a local limit Theorem for cocycles with moderate deviations due to Benoist-Quint (2016), that is of independent interest.
Keywords
Cite
@article{arxiv.2109.13017,
title = {Logarithmic Fourier decay for self conformal measures},
author = {Amir Algom and Federico Rodriguez Hertz and Zhiren Wang},
journal= {arXiv preprint arXiv:2109.13017},
year = {2022}
}
Comments
V2: Improved the structure and presentation, and clarified some of the arguments, following the referee report. Main results unchanged. To appear in JLMS