Institute of Mathematics Conferences, Sixth International Conference on Analytic Number Theory and Spatial Tessellations

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On metric and dimensional theories of ICS-expansions
Olha Vaskova, Grygoriy Torbin

Building: Mykhailo Drahomanov National Pedagogical University
Room: Room C
Date: 2018-09-27 05:05 PM – 17:20
Last modified: 2018-09-22

Abstract


We introduce the ICS-expansion of real numbers which contains as a rather special cases the classical Cantor series expansions and alternative Cantor series expansions. We  found necessary and sufficient conditions for the family of cylinders of the  ICS-expansion to be faithful for the Hausdorff dimension calculation on the unit interval.  We also prove that the mapping which maps digits of the classical Cantor expansion into the same digits of the ICS-expansion preserves the Hausdorff dimension (i.e., it is a G-isomorphism in terms of Harko-Nikiforov-Torbin papers).