2023/07/26 by André Carvalho, Carvalho, André
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2307.13875
openalex publication_date 2023/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that Brinkmann's problems are decidable for endomorphisms of Fn× Fm: given (x,y),(z,w)∈ Fn× Fm and Φ∈ End(Fn× Fm), it is decidable whether there is some k∈ ℕ such that (x,y)Φk=(z,w) (or (x,y)Φk∼(z,w)). We also prove decidability of a two-sided version of Brinkmann's conjugacy problem for injective endomorphisms which, from the work of Logan, yields a solution to the conjugacy problem in ascending HNN-extensions of Fn× Fm. Finally, we study the dynamics of automorphisms of Fn× Fm at the infinity, proving that that their dynamics at the infinity is asymptotically periodic, as occurs in the free and free-abelian times free cases.