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For a large class of irreducible shift spaces $XsubsettA^{Z^d}$, with $tA$ a finite alphabet, and for absolutely summable potentials $Phi$, we prove that equilibrium measures for $Phi$ are weak Gibbs measures. In particular, for $d=1$, the result holds for irreducible sofic shifts.
Let (X,T) be a dynamical system, where X is a compact metric space and T a continuous onto map. For weak Gibbs measures we prove large deviations estimates.
We prove a comprehensive version of the Ruelle-Perron-Frobenius Theorem with explicit estimates of the spectral radius of the Ruelle transfer operator and various other quantities related to spectral properties of this operator. The novelty here is t
This paper has been withdrawn by the authors due to an error in the main theorem.
Let $G=leftlangle S|R_{A}rightrangle $ be a semigroup with generating set $ S$ and equivalences $R_{A}$ among $S$ determined by a matrix $A$. This paper investigates the complexity of $G$-shift spaces by yielding the topological entropies. After reve
We consider suspension flows with continuous roof function over the full shift $Sigma$ on a finite alphabet. For any positive entropy subshift of finite type $Y subset Sigma$, we explictly construct a roof function such that the measure(s) of maximal