Cocyclic subshifts

Motivated by the computations in the theory of cohomological Conley index, cocyclic subshifts are the supports of locally constant matrix cocycles on the full shift over a finite alphabet. They properly generalize sofic systems and topological Markov chains; and, via the Wedderburn-Artin theory of finite-dimensional algebras, admit a similar structure theory with a spectral decomposition into mixing components. These components have specification, which implies intrinsic ergodicity and entropy generation by sequences of horseshoes. Also, a zeta-like generating function for cocyclic subshifts leads to simple criteria for existence of a factor map onto the full two-shift - which gives practical tools for detecting chaos in general discrete dynamical systems.