2021/05/02 by Sieye Ryu, Ryu, Sieye
Computer Science · Mathematics · #37B05 #Advanced Combinatorial Mathematics #Cellular Automata and Applications #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Primary 37B10 #Secondary 15A18 #math.CO #math.DS #msc:15A18 #msc:37B05 #msc:37B10
paper · pdf · doi:10.48550/arxiv.2105.00423
29 pages
openalex publication_date 2021/05/02 · arxiv created 2021/05/13 · arxiv updated 2021/05/17 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
A D∞-topological Markov chain is a topological Markov chain provided with an action of the infinite dihedral group D∞. It is defined by two zero-one square matrices A and J satisfying AJ=JA^\textsfT and J2=I. Flip signature is obtained from symmetric bilinear forms with respect to J on the eventual kernel of A. We modify Williams' decomposition theorem to prove flip signature is a D∞-conjugacy invariant. We introduce natural D∞-actions on Ashley's eight-by-eight and the full two-shift. The Flip signatures show that Ashley's eight-by-eight and the full two-shift equipped with the natural D∞-actions are not D∞-conjugate. We also discuss the notion of D∞-shift equivalence and the Lind zeta function.