Almost Markov and shift equivalent sofic systems - Boyle, McBlaine Michael; Krieger, Wolfgang (Dynamical Systems, 1988)
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.