Fourier decay of equilibrium states for bunched attractors

Abstract

Abstract Let M be a closed manifold, and let f : M → M be a C 2 + α Axiom A diffeomorphism. Suppose that f has an attractor Ω 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 Ω. 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.