Limit Sets and Internal Transitivity in Free Group Actions

2019/08/20 by Kyle Binder, Binder, Kyle, Jonathan Meddaugh +1
Economics, Econometrics and Finance · Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #Economic theories and models #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1908.07382

openalex publication_date 2019/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It has been recently shown that, under appropriate hypotheses, the ω-limit sets of a dynamical system are characterized by internal chain transitivity. In this paper, we examine generalizations of these ideas in the context of the action of a finitely generated free group or monoid. We give general definitions for several types of limit sets and analogous notions of internal transitivity. We then demonstrate that these limit sets are completely characterized by internal transitivity properties in shifts of finite type and general dynamical systems exhibiting a form of the shadowing property.

Citations

• ω-Limit sets for Axiom A diffeomorphisms
• The undecidability of the domino problem

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