Fourier transform and expanding maps on Cantor sets

2020/09/03 by Sahlsten, Tuomas, Stevens, Connor · 2 citations
#Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.01703

Abstract

We study the Fourier transforms \widehatμ(ξ) of non-atomic Gibbs measures μ for uniformly expanding maps T of bounded distortions on [0,1] or Cantor sets with strong separation. When T is totally non-linear, then \widehatμ(ξ) → 0 at a polynomial rate as |ξ| → ∞.

Cited by

• Decomposition of real numbers into sums of Lüroth sets
• Fourier decay in parabolic C^1+α systems with overlaps

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