Monotonicity of the Set of Zeros of Lyapunov Exponent with Respect to Shift Embeddings

We consider the discrete Schrödinger operators with potentials whose values are read along the orbits of a shift of finite type. We study a certain subset of the collection of energies at which the Lyapunov exponent is zero and prove monotonicity of this set with respect to the shift embeddings. Then we introduce a certain function \(\mathcal{J}\) $\mathcal{J}$ (A, μ) determined by the position of these zeros and prove monotonicity of \(\mathcal{J}\) $\mathcal{J}$ (A, μ) with respect to embeddings