2025/07/03 by Wolfgang Krieger, Krieger, Wolfgang · 1 citation
Engineering · Mathematics · #37B10 #Advanced Differential Equations and Dynamical Systems #Aperiodic graph #Dynamical Systems (math.DS) #Embedding #Entropy (arrow of time) #Ergodic theory #FOS: Mathematics #Material Science and Thermodynamics #Mathematical Dynamics and Fractals #Subshift of finite type #Topological dynamics #Topological entropy #Topological entropy in physics
paper · pdf · doi:10.48550/arxiv.2507.02717
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/07/03 · openalex created_date 2025/10/12 · openalex updated_date 2026/08/05
For an aperiodic subshift of finite type Y and for a subshift X with topological entropy less than the topological entropy of Y, a theorem is proved in Krieger: On the subsystems of topological Markov chains, Ergodic Theory & dynamical systems 1982 \bold2, 195-202, that says that the necessary condition on the periodic points of X and Y for the existence of an embedding of X into Y is also sufficient for the existence of an embedding of X into Y. In this note we point out that this theorem extends to certain classes of sofic shifts as target shifts.