Multifractal spectra of multi-affine functions

Albert László Barabási*, Péter Szépfalusy, Tamás Vicsek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

Self-affine functions F(x) with multiscaling height correlations cq(x) ∼xqHq are described in terms of the standard multifractal formalism with a modified assumption for the partition. The corresponding quantities and expressions are shown to exhibit some characteristic differences from the standard ones. According to our calculations the f(α) type spectra are not uniquely determined by the Hq spectrum, but depend on the particular choice which is made for the dependence of N on x, where N is the number of points over which the average is taken. Our results are expected to be relevant in the analysis of signal type data obtained in experiments on systems with an underlying multiplicative process.

Original languageEnglish
Pages (from-to)17-28
Number of pages12
JournalPhysica A: Statistical Mechanics and its Applications
Volume178
Issue number1
DOIs
StatePublished - 1 Oct 1991
Externally publishedYes

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