Quasi-fixed points of substitutive systems

Autor:	Krawczyk, Elżbieta
Rok vydání:	2024
Předmět:	Mathematics - Combinatorics Mathematics - Dynamical Systems Primary: 11B85 37B10 68R15. Secondary: 68Q45
Druh dokumentu:	Working Paper
Popis:	We study automatic sequences and automatic systems generated by general constant length (nonprimitive) substitutions. While an automatic system is typically uncountable, the set of automatic sequences is countable, implying that most sequences within an automatic system are not themselves automatic. We provide a complete and succinct classification of automatic sequences that lie in a given automatic system in terms of the quasi-fixed points of the substitution defining the system. Our result extends to factor maps between automatic systems and highlights arithmetic properties underpinning these systems. We conjecture that a similar statement holds for general nonconstant length substitutions. Comment: 27 pp
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.01974 Zobrazit plný text záznamu View this record from Arxiv