Continuous transformations preserving tails of an $A$-continued fraction representation of numbers

Artem Chuikov; Mykola Pratsiovytyi

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

Artem Chuikov, Mykola Pratsiovytyi

Building: Mykhailo Drahomanov National Pedagogical University
Room: Room C
Date: 2018-09-28 04:45 PM – 17:00
Last modified: 2018-09-24

Abstract

We study continuous strictly monotonic functions preserving tails of $A$-continued fraction representation of real numbers and construct continuous transformations of [0,5; 1]. It is proved that the set of all transformations is infnite and forms a non-commutative group with respect to operation of a superposition.