Assume that $(T, A)$ is a linear cocycle such that $T:X\rightarrow X$ is a homemorphism on compact metric space $X$ and $A:X\rightarrow SL(2, \mathbb{R})$ is a continuous function.

We say that an invariant probability measure $\mu$ is aperiodic for $T$ if set of periodic points of has zero measure.

There is a famous result due to Bochi-Mane that said :

Given any invertible aperiodic ergodic system $(T,\mu)$ on a compact Hausdorff space, every continuous cocycle $A:X→SL(2, \mathbf{R})$ which is not uniformly hyperbolic can be approximated in the $C^{0}$ topology by another whose Lyapunov exponents vanish at $\mu$-almost every point.

Consider the following examples: $$ A_1=diag(2, \frac{1}{2}) , A_{2}=diag(1, 1) $$ $$ A_1=diag(2, \frac{1}{2}) , A_{2}=antidiag(1, 1)$$ Would one show me how to approximate the above linear cocycles such that it has zero Lyapunov exponent?