In this paper, we describe the relationship between Perron root and eigenvectors of an irreducible subshift finite type with correlation forbidden words in subshift. particular, derive expression for associated adjacency matrix. As application, obtain (0,1) matrices which are directed graphs. Moreover, alternate definition Parry measure ergodic theory on type.

In this article we prove an analogue of Bauer’s theorem from algebraic number theory in the context of hyperbolic systems. 0. Introduction Let φ : X → X be a hyperbolic dynamical system and, for a finite G, let φ̃ : X̃ → X̃ be a G-extension for which φ̃ is also hyperbolic. Given φ we are interested in describing the possibilities for φ̃ in terms of the closed φ-orbits. This is analogous to a classic...