Sequences close to periodic

TL;DR

This survey explores various generalizations of periodic sequences across multiple fields including combinatorics, dynamics, logic, and number theory, highlighting recent developments and connections.

Contribution

It provides a comprehensive overview of classical and new notions of periodicity, integrating diverse perspectives and recent research results.

Findings

Summarizes key concepts of almost periodicity in different domains

Highlights recent advances in the theory of generalized periodic sequences

Connects periodicity notions across multiple mathematical fields

Abstract

The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical theories, algorithmic computability, Kolmogorov complexity, number theory, are discussed.