Variational principles for the topological pressure of measurable potentials

Marc Rauch

doi:10.3934/dcdss.2017018

Article Contents

2017, Volume 10, Issue 2: 367-394. Doi: 10.3934/dcdss.2017018

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Variational principles for the topological pressure of measurable potentials

Marc Rauch^,

Mathematical Institute, University of Jena, Ernst-Abbe-Platz 2,07745 Jena, Germany

* Corresponding author: Marc Rauch
* Corresponding author: Marc Rauch

Received: September 30, 2015

Revised: October 31, 2016

Published: February 2018

This work was supported by the Deutsche Forschungsgemeinschhaft

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Abstract

We introduce notions of topological pressure for measurable potentials and prove corresponding variational principles. The formalism is then used to establish a Bowen formula for the Hausdorff dimension of cookie-cutters with discontinuous geometric potentials.

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Mathematics Subject Classification: Primary: 37B99; Secondary: 28A80.

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Figure 1. A cookie cutter with discontinuous geometric potentials

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Figure 2. The function $T_i(x)$ for $\epsilon=1/8$

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Figure 3. The cookie-cutters $T_n$ approaching the limit cookie-cutter $T_\infty$

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