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Average Topological Pressure and a Variational Principle

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Abstract

In this paper, we define a new version of topological pressure, called average topological pressure, for dynamical systems. We present some of its properties and prove an Abramov-Rokhlin-like relation using the new defined quantity. It connects the topological pressure of the skew product of a random dynamical system to the topological entropy of the noise map and the average topological pressure. The topological pressure of random dynamical systems is connected to the average topological pressure via a variational principle.

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Acknowledgements

The authors would like to thank the referees for their comprehensive and useful comments which helped the improvement of this work to the present form.

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  1. Mehdi Rahimi and Asghar Ghodrati contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran

    Mehdi Rahimi & Asghar Ghodrati

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  1. Mehdi Rahimi
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  2. Asghar Ghodrati
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Correspondence to Mehdi Rahimi.

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Rahimi, M., Ghodrati, A. Average Topological Pressure and a Variational Principle. J Dyn Control Syst (2024). https://doi.org/10.1007/s10883-024-09688-y

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  • DOI: https://doi.org/10.1007/s10883-024-09688-y

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