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arXiv · 1810.01378

Fourier decay in nonlinear dynamics

Tuomas Sahlsten·Connor Stevens
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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).

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Tuomas Sahlsten, Connor Stevens. 2018-10-02. Fourier decay in nonlinear dynamics. https://arxiv.org/abs/1810.01378

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