POSITIVE LYAPUNOV EXPONENT FOR A CLASS OF QUASI-PERIODIC COCYCLES

摘要

Young [17] proved the positivity of Lyapunov exponent in a large set of the energies for some quasi-periodic cocycles. Her result is also proved to be applicable for some quasi-periodic Schroedinger cocycles by Zhang [18]. However, her result cannot be applied to the Schrodinger cocycles with the potential v = cos(4πx) + w(x), where w ∈ C~2(R/Z,R) is a small perturbation. In this paper, we will improve her result such that it can be applied to more cocycles.