Normal sequences with given limits of multiple ergodic averages

Lingmin Liao; Michał Rams

doi:10.5565/PUBLMAT6512108

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.

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Lingmin Liao. Michał Rams. "Normal sequences with given limits of multiple ergodic averages." Publ. Mat. 65 (1) 271 - 290, 2021. https://doi.org/10.5565/PUBLMAT6512108

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Received: 25 September 2019; Revised: 10 September 2020; Published: 2021

First available in Project Euclid: 11 December 2020

MathSciNet: MR4185833

Digital Object Identifier: 10.5565/PUBLMAT6512108

Subjects:

Primary: 28A80

Secondary: 11K16 , 37B40

Keywords: Hausdorff dimension , multiple ergodic averages , normal sequences , topological entropy

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