In the past decades, rich results on dynamical and spectral properties of analytic quasi-periodic Schrodinger operators (QPSO), like positivity and regularity of Lyapunov exponents, almost reducibility and almost localization, Cantor spectrum etc., have been obtained. The methods among these results depend heavily on the regularity condition.  On the other hand, recently we obtained the counterpart of the above results for C2 large-coupling QPSO imposed with a so called cos-like geometry condition on the potentials. Among them, some property is even not true for general analytic QPSO. In this talk, we will discuss the roles played by regularity condition and geometry condition in QSPO.

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