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

2021/03/30 by Fernando José Sánchez-Salas, Sánchez-Salas, Fernando José
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Geometric and Algebraic Topology #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2103.16373

Abstract

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

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