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Polynomial Fourier decay and a cocycle version of Dolgopyat's method for self conformal measures

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arxiv 2306.01275 v2 pith:QDJYHO3S submitted 2023-06-02 math.DS math.CA

Amir Algom , Federico Rodriguez Hertz , Zhiren Wang This is my paper · ORCID
classification math.DSmath.CA
keywords decaypolynomialcocycleconformaldolgopyateveryfouriermathbb
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abstract

We show that every self conformal measure with respect to a $C^2 (\mathbb{R})$ IFS $\Phi$ has polynomial Fourier decay under some mild and natural non-linearity conditions. In particular, every such measure has polynomial decay if $\Phi$ is $C^\omega (\mathbb{R})$ and contains a non-affine map. A key ingredient in our argument is a cocycle version of Dolgopyat's method, that does not require the cylinder covering of the attractor to be a Markov partition. It is used to obtain spectral gap-type estimates for the transfer operator, which in turn imply a renewal theorem with an exponential error term in the spirit of Li (2022).

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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