Generalization of multifractal theory within quantum calculus

  title={Generalization of multifractal theory within quantum calculus},
  author={Alexander I. Olemskoi and I. {\`A}. Shuda and Vadim Borisyuk},
On the basis of the deformed series in quantum calculus, we generalize the partition function and the mass exponent of a multifractal, as well as the average of a random variable distributed over a self-similar set. For the partition function, such expansion is shown to be determined by binomial-type combinations of the Tsallis entropies related to manifold deformations, while the mass exponent expansion generalizes the known relation τq=Dq(q-1). We find the equation for the set of averages… 

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