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arXiv · 2609.17743

Fourier Decay of SRB Measures for Skew Products

Gaétan Leclerc·Haojie Ren
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Abstract

We study Fourier decay of natural invariant measures for real analytic skew products $T(x,y)=(f(x),g(x,y))$ on $\mathbb{S}^1 \times [-1,1]$, where $f$ is expanding and $0<|\partial_y g(x,y)|<1$. Let $\mathcal S$ denote the associated solenoidal attractor. We prove a dichotomy: either $\mathcal S$ is a single horizontal graph, or both the SRB measure and the measure of maximal entropy have polynomial Fourier decay. No transversality assumption is imposed.

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Gaétan Leclerc, Haojie Ren. 2026-09-15. Fourier Decay of SRB Measures for Skew Products. https://arxiv.org/abs/2609.17743

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