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On the variational principle for the topological pressure for certain non-compact sets

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Abstract

Let (X, d, T) be a dynamical system, where (X, d) is a compact metric space and T: X → X is a continuous map. We assume that the dynamical system satisfies g-almost product property and the uniform separation property. We compute the topological pressure of saturated sets under these two conditions. If the uniform separation property does not hold, we compute the topological pressure of the set of generic points. We give an application of these results to multifractal analysis and finally get a conditional variational principle.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University, Nanjing, 210097, China

    Yu Pei & ErCai Chen

  2. Center for Nonlinear Science, Nanjing University, Nanjing, 210093, China

    ErCai Chen

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  1. Yu Pei
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  2. ErCai Chen
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Correspondence to ErCai Chen.

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Pei, Y., Chen, E. On the variational principle for the topological pressure for certain non-compact sets. Sci. China Math. 53, 1117–1128 (2010). https://doi.org/10.1007/s11425-009-0109-4

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  • DOI: https://doi.org/10.1007/s11425-009-0109-4

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