# American Institute of Mathematical Sciences

April  2017, 10(2): 367-394. doi: 10.3934/dcdss.2017018

## Variational principles for the topological pressure of measurable potentials

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

* Corresponding author: Marc Rauch

Received  October 2015 Revised  November 2016 Published  January 2017

Fund Project: This work was supported by the Deutsche Forschungsgemeinschhaft.

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.

Citation: Marc Rauch. Variational principles for the topological pressure of measurable potentials. Discrete & Continuous Dynamical Systems - S, 2017, 10 (2) : 367-394. doi: 10.3934/dcdss.2017018
##### References:

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##### References:
A cookie cutter with discontinuous geometric potentials
The function $T_i(x)$ for $\epsilon=1/8$
The cookie-cutters $T_n$ approaching the limit cookie-cutter $T_\infty$
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