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A Variational Principle of the Topological Pressures for Non-autonomous Iterated Function Systems

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Abstract

In this paper, the definitions of measure-theoretic pressures, Pesin–Pitskel topological pressures and weighted topological pressures are introduced for non-autonomous iterated function systems. It is shown that Pesin–Pitskel topological pressures and weighted topological pressures coincide. The main purpose of this paper is to establish a variational principle between the Pesin–Pitskel topological pressure and the measure-theoretic pressure of Borel probability measures for non-autonomous iterated function systems.

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Acknowledgements

The authors are grateful to the referee for a careful reading of the paper and a multitude of corrections and helpful suggestions.

Funding

This work is supported by National Natural Science Foundation of China (12271432).

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710127, People’s Republic of China

    Mengxin Cui & Zhiming Li

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  1. Mengxin Cui
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  2. Zhiming Li
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MC was responsible for conceptualization and writing the original draft. ZL took part in supervision, and writing, reviewing and editing the manuscript.

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Correspondence to Zhiming Li.

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Cui, M., Li, Z. A Variational Principle of the Topological Pressures for Non-autonomous Iterated Function Systems. Qual. Theory Dyn. Syst. 22, 150 (2023). https://doi.org/10.1007/s12346-023-00848-2

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  • DOI: https://doi.org/10.1007/s12346-023-00848-2

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