A group of continuous transformations of a region $[0; 1]$ that preserve the frequency of the digits in $Q_s$-representation of a number

• Date: 2017
• Author Affiliations: Р. Ю. Осауленко — Інститут математики НАН України
• Keywords: keywords
• Main Authors: Osaulenko, R. Yu., Осауленко, Р. Ю.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2017
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/53
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

In the paper, we propose to solve the problem of construction a set of a continuous transformation of the segment $[0;1]$, which keeps the figure frequency of a $????_????$ real number representation for any natural $???? >1$. The group properties of that set are studied in the article. S...