Anderson localization for CMV matrices with Verblunsky coefficients defined by the hyperbolic toral automorphism

In this paper, we prove the large deviation estimates and Anderson localization for CMV matrices on ${\ell }^2\left(Z_{+}\right)$ with Verblunsky coefficients defined dynamically by the hyperbolic toral automorphism. Part of positivity results on the Lyapunov exponents of Chulaevsky-Spencer [9] and Anderson localization results of Bourgain-Schlag [6] on Schrödinger operators with strongly mixing potentials are extended to CMV matrices.