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Dimension estimates for arbitrary subsets of limit sets of a Markov construction and related multifractal analysis. (English) Zbl 1319.37014

The authors obtain estimates for the dimension of any subset of a limit set of a Markov construction, using properties of Markov partitions and without constructing any measure. Furthermore, they investigate the dimensions of asymptotically conformal repellers and also the dimension spectrum of the level sets of nonadditive potentials on asymptotically conformal repellers.

MSC:

37C45 Dimension theory of smooth dynamical systems
37D35 Thermodynamic formalism, variational principles, equilibrium states for dynamical systems
37B10 Symbolic dynamics
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