We explore Avila's global theory for one-frequency Schr?dinger operators from the point of view of Aubry duality. We establish the one-to-one correspondence between the Lyapunov exponent of the Schr?dinger cocycles and the Lyapunov exponents of its dual cocycles. We also give a new equivalent definition of subcritical, critical, supercritical regimes. Especially, we prove that the acceleration of the Schr?dinger cocycle equals to the pair of zero Lyapunov exponents of its dual cocycle. Finally, we talk about its physical application.
