Density of positive Lyapunov exponents for symplectic cocycles

We prove that Sp(2d, R)-cocycles, HSp(2d)-cocycles and pseudo-unitary cocycles with at least one non-zero Lyapunov exponent are dense in all usual regularity classes for non-periodic dynamical systems. For Schrodinger operators on the strip, we prove a similar result about the density of positive Lyapunov exponents. This generalizes a result of A. Avila [2] to higher dimensions.
QC 20190830