Abstract
One knows that the set of quasi-periodic Schrodinger cocycles with positive Lyapunov exponent is open and dense in analytic topology. In this paper, we construct cocycles with positive Lyapunov exponent which can be arbitrarily approximated by ones with zero Lyapunov exponent in the space of $${\mathcal{C}^ l (1 \le l \le \infty)}$$ smooth quasi-periodic cocycles, which shows that the set of quasi-periodic Schrodinger cocycles with positive Lyapunov exponent is not open in smooth topology.
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