We attempt to prove positivity of the Lyapunov exponent for
the one-dimensional, discrete, quasi-periodic Schrodinger operator in the
very general case of a smooth, non-transversal (e.g. non-flat at any
point) potential function. This result would hold for all energies. The
method used improves on some techniques developed recently by K. Bjerklov.
These techniques are reminiscent of the ones used to study the dynamics of
the Henon map by M. Benedicks and L. Carleson.