Normal numbers with given limits of multiple ergodic averages

Abstract

We are interested in the set of normal sequences in the space $\{0,1{\}}^{\mathbb{N}}$ with a given frequency of the pattern $11$ in the positions $k,2k$. The topological entropy of such sets is determined.

20 pages. A section Preliminary is added. More details of the proofs are given

References in corpus (1)

• Level sets of multiple ergodic averages