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Local Pressure of Subsets and Measures

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Abstract

In this paper, we study various notions of local pressure of subsets and measures with respect to a fixed open cover, which are defined by Carathéordory–Pesin construction. We show that all local pressures of an ergodic measure equal the local metric entropy defined by Romagnoli (Ergod Theory Dyn Syst, 23(05):1601–1610, 2003) plus the integral of potential up to a variation of potential with respect to the open cover. In particular, this answers positively a question by Downarowicz (Entropy in dynamical systems, New Mathematical Monographs, vol 18, Cambridge University Press, xii+391, 2011) on variant entropy. As analogs of local variational principles, we also establish variational inequalities for local pressure of subsets.

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Acknowledgements

This work is supported by NSFC Nos. 12071474 and 11701559.

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  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, People’s Republic of China

    Weisheng Wu

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  1. Weisheng Wu
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Correspondence to Weisheng Wu.

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Communicated by Eric A. Carlen.

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Wu, W. Local Pressure of Subsets and Measures. J Stat Phys 185, 9 (2021). https://doi.org/10.1007/s10955-021-02822-1

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