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New Bounds for the Hausdorff Dimension of a Dynamically Defined Cantor Set
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: 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 $M$.
Keywords
non conformal repellers; dimension theory; thermodynamic formalism
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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