Periodic points and automorphisms of the shift - Boyle, McBlaine Michael; Krieger, Wolfgang (Transactions of the American Mathematical Society, 1987)
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 symbols which can be extended to a composition of involutions of the shift.