2022/08/01 by Arnaud Hilion, Hilion, Arnaud, Gilbert Levitt +1
Computer Science · Mathematics · #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2208.00676
openalex publication_date 2022/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inspired by Pansiot's work on substitutions, we prove a similar theorem for automorphisms of a free group F of finite rank: if a right-infinite word X represents an attracting fixed point of an automorphism of F, the subword complexity of X is equivalent to n, n log log n, n log n, or n2. The proof uses combinatorial arguments analogue to Pansiot's as well as train tracks. We also define the recurrence complexity of X, and we apply it to laminations. In particular, we show that attracting laminations have complexity equivalent to n, n log log n, n log n, or n2 (to n if the automorphism is fully irreducible).