Profinite semigroups
Revekka Kyriakoglou, Dominique Perrin
TL;DR
This paper surveys the theory of profinite semigroups and their connections to symbolic dynamics, highlighting key results and including some original findings on Schützenberger groups in recurrent sets.
Contribution
It provides a comprehensive overview of profinite semigroups and introduces new results on Schützenberger groups linked to recurrent sets.
Findings
Summarizes key results on profinite semigroups and symbolic dynamics.
Introduces original results on Schützenberger groups in recurrent sets.
Connects algebraic structures with dynamical systems.
Abstract
We present a survey of results on profinite semigroups and their link with symbolic dynamics. We develop a series of results, mostly due to Almeida and Costa and we also include some original results on the Sch\"utzenberger groups associated to a uniformly recurrent set.
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Taxonomy
Topicssemigroups and automata theory · Mathematical Dynamics and Fractals · Geometric and Algebraic Topology