Fundamental Properties of “Homogeneous” Multifractals<sup>*</sup>

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  • Fundamental Properties of “Homogeneous” Multifractals
  • Fundamental Properties of Homogeneous M

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It is proven from the requirement of scale-similarity of multifractals that the probability of spatial distribution of a certain measure supported by a multifractal, which may be called intrinsic probability, is uniquely determined for a scale ratio tending to zero if the f-α spectrum of the multifractal is given. As a corollary, it is proven that there exists no nonlinear transformation of multifractals. Also, it is derived that intrinsic probabilities of many multifractals including multinomial generalized Cantor sets can be determined by the knowledge of intermittency exponents μ(q) (and then generalized dimensions D(q)) limited for q=nonnegative integers only.

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