Monotonicity of the set of zeros of the Lyapunov exponent with respect to shift embeddings

Abstract: We consider the discrete Schr\"odinger 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 ${\mathcal J}(A,\mu)$ determined by the position of these zeros and prove monotonicity of ${\mathcal J}(A,\mu)$ with respect to embeddings.