Shift spaces, Languages and Transfinite Induction
Dynamical Systems
2024-02-13 v4
Abstract
This paper deals with an extension of the classical concept of shift space, which corresponds to any shift-invariant closed subset of the Cartesian product of a particular finite set (alphabet) endowed with the prodiscrete topology. In such an extended framework the notion of language is introduced and a characterization is shown. In order to do this, transfinite induction is required because the cardinality of the index set of the product may not be countable.
Keywords
Cite
@article{arxiv.2308.10352,
title = {Shift spaces, Languages and Transfinite Induction},
author = {Maira Aranguren and Jorge Campos and Neptalí Romero and Ramón Vivas},
journal= {arXiv preprint arXiv:2308.10352},
year = {2024}
}