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arXiv · 2301.10623

Fourier decay of equilibrium states for bunched attractors

Gaétan Leclerc
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Abstract

Let $M$ be a closed manifold, and let $f:M \rightarrow M$ be a $C^{2+\alpha}$ Axiom A diffeomorphism. Suppose that $f$ has an attractor $\Omega$ with codimension 1 stable lamination. Under a generic nonlinearity condition and a suitable bunching condition, we prove polynomial Fourier decay in the unstable direction for a large class of invariant measures on $\Omega$. Our result applies in particular for the measure of maximal entropy. We construct in the appendix an explicit solenoid that satisfies the nonlinearity and bunching assumption.

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Gaétan Leclerc. 2023-01-25. Fourier decay of equilibrium states for bunched attractors. https://arxiv.org/abs/2301.10623

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