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Classifying Cantor sets by their multifractal spectrum

2010; IOP Publishing; Volume: 23; Issue: 11 Linguagem: Inglês

10.1088/0951-7715/23/11/011

1361-6544

Kathryn E. Hare, Leandro Zuberman,

Mathematical Dynamics and Fractals

The multifractal spectrum of a measure is the dimension of the sets In this work we focus on Cantor measures μ and the Cantor sets which support them. We consider the more general sets, , defined by replacing rα by h(r), and the sets, , formed by functions h for which a given element x belongs to . We propose a classification for the Cantor sets in terms of the sets that is finer than the classification by dimension, but not as fine as the classification given by the equivalence of associated dimension functions. We characterize this latter classification in terms of particular subsets of .