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

Анотація

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).