Systems of encoding of real numbers with infinite alphabet and mathematical objects with fractal properties.

Authors

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

Keywords:

Systems of encoding of real numbers, Sylvester series, Ostrogradsky series

Abstract

The objects with a special topological and metric structure and fractal properties arise in the study of transformations and mappings. Transformations preserving fractal dimension (like a Hausdorff–Besicovitch dimension) of all Borel subsets of unit interval as well as mappings preserving tails of representation and frequency of digits form a group with respect to the operation of composition (superposition).

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