PreprintCC BY 4.0arXiv
Fourier Decay of SRB Measures for Skew Products
Abstract
We study Fourier decay of natural invariant measures for real analytic skew products T(x,y)=(f(x),g(x,y)) on 𝕊1 × [−1,1], where f is expanding and 0<|∂y g(x,y)|<1. Let 𝒮 denote the associated solenoidal attractor. We prove a dichotomy: either 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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BibTeX
@misc{leclerc2026fourier,
title = {{Fourier Decay of SRB Measures for Skew Products}},
author = {Gaétan Leclerc and Haojie Ren},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17743},
eprint = {2609.17743},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17743},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fourier Decay of SRB Measures for Skew Products
AU - Gaétan Leclerc
AU - Haojie Ren
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17743
UR - https://arxiv.org/abs/2609.17743
AB - We study Fourier decay of natural invariant measures for real analytic skew products T(x,y)=(f(x),g(x,y)) on 𝕊^1 × [−1,1], where f is expanding and 0<|∂_y g(x,y)|<1. Let 𝒮 denote the associated solenoidal attractor. We prove a dichotomy: either 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.
ER -