Fourier decay of equilibrium states for bunched attractors

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.