Abstract: Anderson localization is a physical phenomenon that was observed by Phillip Anderson. One definition of localization is when the spectrum of the Schrödinger operator has pure point spectrum with exponentially decaying eigenfunctions. The Lyapunov exponent plays a central role in studying the phenomenon, as uniformly positive Lyapunov exponents paired with a large deviation estimate has been a large indication of localization. Our focus is when one can prove uniform positivity, as Kotani theory would imply that the family of Schrödinger operators has an empty absolutely continuous spectrum. In our talk, we discuss the setting and the methods used to show uniformly positive Lyapunov exponents for lower Hölder potentials along local unstable leaves when generated by hyperbolic dynamics with at least one expanding direction.