English

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 {0,1}N\{0,1\}^\mathbb{N} with a given frequency of the pattern 1111 in the positions k,2kk, 2k. The topological entropy of such sets is determined.

Keywords

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

R2 v1 2026-06-23T08:51:08.818Z