Working Paper Article Version 1 This version is not peer-reviewed

New Bounds for the Hausdorff Dimension of a Dynamically Defined Cantor Set

Version 1 : Received: 31 March 2021 / Approved: 2 April 2021 / Online: 2 April 2021 (13:53:28 CEST)

How to cite: Sánchez-Salas, F.J. New Bounds for the Hausdorff Dimension of a Dynamically Defined Cantor Set. Preprints 2021, 2021040063 Sánchez-Salas, F.J. New Bounds for the Hausdorff Dimension of a Dynamically Defined Cantor Set. Preprints 2021, 2021040063

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 piecewise smooth expanding maps on a $d$-dimensional smooth manifold $M$.

Subject Areas

non conformal repellers; dimension theory; thermodynamic formalism

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