New bounds for the Hausdorff dimension of a dynamically defined Cantor set

Abstract

In this paper we use the additive thermodynamic formalism to obtain new bounds of the Hausdorff and box-counting dimension of certain non conformal hyperbolic repellers defined by $C^r$, $r>1$ piecewise expanding maps on a $d$-dimensional smooth manifold $M$.

arXiv commentThis is a new version of a previous preprint with a number of corrections and improvements