Hausdorff dimension of thin higher-dimensional solenoidal attractors

Abstract

Abstract In this work we study the Hausdorff dimension of hyperbolic attractors that are given by skew-products. We prove that if the contraction is sufficiently strong, the weak-contraction is conformal and the attractor satisfies a geometric condition of transversality between its components, then the Hausdorff dimension and the box-counting dimension of the attractor satisfy Bowen’s formula. We also prove that for any attractor whose contraction is sufficiently strong, there exist dynamics C r -close such that the Hausdorff dimension and the box-counting dimension of the attractor have the same value given by Bowen’s formula.