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Associated to $\\phi \\in \\text{Aut}(\\sigma_{A})$ are certain Lyapunov exponents $\\alpha^{-}(\\phi), \\alpha^{+}(\\phi)$ which describe asymptotic behavior of the sequence of coding ranges of $\\phi^{n}$. We give lower bounds on $\\alpha^{-}(\\phi), \\alpha^{+}(\\phi)$ in terms of the spectral radius of the corresponding action of $\\phi$ on the dimension group associated to $(X_{A},\\sigma_{A})$. 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