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Dimension estimates for arbitrary subsets of limit sets of a Markov construction and related multifractal analysis

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  • Without constructing any measure and using properties of Markov partition, this paper provides a direct proof of dimension estimates for any subset of a limit set of a Markov construction. Furthermore, this paper investigate the dimensions of asymptotically conformal repellers. And the dimension spectrum of the level sets of nonadditive potentials on asymptotically conformal repellers are also obtained.
    Mathematics Subject Classification: Primary: 37C45, 37D35; Secondary: 37B10.

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