Abstract
This paper gives a method to obtain Hausdorff dimensions of sub-self-similar sets, where the ratios of similitudes are different. By using Gibbs measure and pressure in the sense of thermodynamic formalism, we obtain the Hausdorff dimensions of sub-self-similar sets in the space of infinite sequences. We then consider sub-self-similar sets in Rd and show how to calculate their Hausdorff dimensions under an open set condition.
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