Algebraic structures in the theory of fractals (fractal geometry and fractal analysis).

Authors

  • M. Pratsiovytyi Institute of Mathematics of NASU, National Pedagogical Dragomanov University, Kyiv, Ukraine

Keywords:

Fractal, self-affine set, function with fractal properties, transformation preserving fractal dimension, singular probability distribution, system of encoding (representation) of real numbers

Abstract

The fractal is a set of complete metric space that have the property of self-similarity in some sense (classic self-similarity, self-affinity or “structural similarity”) or have fractional metric dimension (like a Hausdorff–Besicovitch or Minkowski dimension, entropic or box-counting dimension) as well as such that its metric and topological dimension are unequal.

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