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Topological Pressure of Free Semigroup Actions For Non-Compact Sets and Bowen’s Equation, II

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Abstract

Inspired to the work of Ma and Wu (Discrete Contin Dyn Syst 31:545–557, 2011) and Climenhaga (Ergodic Theory Dyn Syst 31(4):1163–1182, 2011), we introduce the new notions of topological pressure and upper (lower) capacity topological pressure of a free semigroup action of maps for finite potential functions by using the Carathéodory–Pesin structure (C-P structure) with respect to non-compact sets in this paper. Meanwhile, we also give some properties of these notions. Moreover, by Bowen’s equation, we characterize the Hausdorff dimension of certain sets, whose points have the positive lower Lyapunov exponents and satisfy a so-called tempered contraction condition.

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Acknowledgements

The authors really appreciate the referees’ valuable remarks and suggestions that helped a lot. The work was supported by National Natural Science Foundation of China (Grant No. 11771149).

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  1. School of Mathematics, South China University of Technology, Guangzhou, 510641, People’s Republic of China

    Qian Xiao & Dongkui Ma

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  1. Qian Xiao
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  2. Dongkui Ma
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Correspondence to Dongkui Ma.

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Xiao, Q., Ma, D. Topological Pressure of Free Semigroup Actions For Non-Compact Sets and Bowen’s Equation, II. J Dyn Diff Equat 35, 2139–2156 (2023). https://doi.org/10.1007/s10884-021-10055-9

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  • DOI: https://doi.org/10.1007/s10884-021-10055-9

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