Fourier decay in nonlinear dynamics
Dynamical Systems
2021-12-06 v2 Classical Analysis and ODEs
Number Theory
Abstract
We study when Fourier transforms of Gibbs measures of sufficiently nonlinear expanding Markov maps decay at infinity at a polynomial rate. Assuming finite Lyapunov exponent, we reduce this to a nonlinearity assumption, which we verify for the Gauss map using Diophantine analysis. Our approach uses large deviations and additive combinatorics, which combines the earlier works on the Gibbs measures for Gauss map (Jordan-Sahlsten, 2013) and Fractal Uncertainty Principle (Bourgain-Dyatlov, 2017).
Cite
@article{arxiv.1810.01378,
title = {Fourier decay in nonlinear dynamics},
author = {Tuomas Sahlsten and Connor Stevens},
journal= {arXiv preprint arXiv:1810.01378},
year = {2021}
}
Comments
This article has been withdrawn as it is superseded by arXiv:2009.01703