1982/06/01 by Wolfgang Krieger · 4 citations
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Cellular Automata and Applications #semigroups and automata theory
paper · pdf · doi:10.1017/s0143385700001516
openalex publication_date 1982/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Abstract Let S A be an irreducible and aperiodic topological Markov chain. If S Ā is an irreducible and aperiodic topological Markov chain, whose topological entropy is less than that of S A , then there exists an irreducible and aperiodic topological Markov chain, whose topological entropy equals the topological entropy at S Ā , and that is a subsystem of S A . If S is an expansive homeomorphism of the Cantor discontinuum, whose topological entropy is less than that of S A , and such that for every j ∈ℕ the number of periodic points of least period j of S is less than or equal to the number of periodic points of least period j of S A , then S is topological conjugate to a subsystem of S A .