Abstract
Using a (weak) Gibbs measure as the reference measure, this paper introduces the concept of q-topological and q-metric pressure following the approach of Carathéodory construction. Some basic properties of q-pressure are given, including the dependence of q-pressure on the parameter q and a formula for the calculation of q-topological pressure. In particular, a relationship between the q-metric pressure and the local metric pressure is established. Finally, the correlation entropy is defined with respect to any invariant measure, and a relationship is obtained between the correlation entropy and the local metric entropy.
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Acknowledgements
The authors are grateful to the anonymous referee for the invaluable comments which helped to improve the manuscript greatly. Yun Zhao and Chiyi Luo are partially supported by The National Key Research and Development Program of China (2022YFA1005802), NSFC (12271386), Qinglan project of Jiangsu Province and NSF of Jiangsu BK20200850. Wen-Chiao Cheng acknowledges the Institute of Mathematics of Academia Sinica for its the hospitality while visiting in the summer of 2022. Wen-Chiao Cheng was partially supported by NSC Grant 110-2115-M-034-001.
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Zhao, Y., Luo, C. & Cheng, WC. q-Pressure for Dynamical Systems. Qual. Theory Dyn. Syst. 22, 104 (2023). https://doi.org/10.1007/s12346-023-00798-9
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DOI: https://doi.org/10.1007/s12346-023-00798-9