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

TL;DR

This paper develops new bounds for the Hausdorff and box-counting dimensions of certain non-conformal hyperbolic repellers using additive thermodynamic formalism, advancing understanding of fractal dimensions in dynamical systems.

Contribution

It introduces novel bounds for fractal dimensions of non-conformal hyperbolic repellers via additive thermodynamic formalism, extending previous results.

Findings

New bounds for Hausdorff dimension of hyperbolic repellers

Bounds applicable to non-conformal, piecewise expanding maps

Enhanced understanding of fractal dimensions in dynamical systems

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 $M$.