Multifractal decomposition of mutual-recursive sets corresponding to a probability and a weight

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  • 相互帰納的集合の確率と重みに対応するマルチフラクタル分析

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Abstract

A random iteration algorithm for mutual-recursive sets (graph-directed sets) is considered. We deal with a pair of a probability and a weight on the mutual-recursive sets. The multifractal decompositions with respect to the pair of probability density and weight density are investigated. Therefore, we introduce a pair of parameters (q, s). Using these parameters, the Hausdorff dimension and the Packing dimension of the set in the mutual-recursive set, of which the densities of probability and weight are specified, are charactrized. This extension of introducing a pair of parameters gives us the freedom to invetigate the spinglass phenomena of multifractal structure as indicated in [4]. This work is an extension of [1], [3] and [4].

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