1987/01/01 by Mike Boyle, Wolfgang Krieger · 2 citations
Mathematics · Computer Science · Physics and Astronomy · #Mathematical Dynamics and Fractals #Cellular Automata and Applications #Chaos control and synchronization
paper · doi:10.1090/s0002-9947-1987-0887501-5
openalex publication_date 1987/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/25
The automorphism group of a topological Markov shift is studied by way of periodic points and unstable sets. A new invariant for automorphisms of dynamical systems, the gyration function, is used to characterize those automorphisms of finite subsystems of the full shift on n symbols which can be extended to a composition of involutions of the shift. It is found that for any automorphism U of a subshift of finite type S, for all large integers M the map USM is a topological Markov shift whose unstable sets equal those of S. This fact yields, by way of canonical measures and dimension groups, information about dynamical properties of USk such as the zeta function and entropy.