Normal numbers with given limits of multiple ergodic averages
Number Theory
2020-07-16 v2 Dynamical Systems
Abstract
We are interested in the set of normal sequences in the space with a given frequency of the pattern in the positions . The topological entropy of such sets is determined.
Cite
@article{arxiv.1904.12143,
title = {Normal numbers with given limits of multiple ergodic averages},
author = {Lingmin Liao and Michał Rams},
journal= {arXiv preprint arXiv:1904.12143},
year = {2020}
}
Comments
20 pages. A section Preliminary is added. More details of the proofs are given