Almost localization and almost reducibility

  title={Almost localization and almost reducibility},
  author={A Guadalupe Rebollo Avila and Svetlana Ya Jitomirskaya},
We develop a quantitative version of Aubry duality and use it to obtain several sharp estimates for the dynamics of Schrödinger cocycles associated to a non-perturbatively small analytic potential and Diophantine frequency. In particular, we establish the full version of Eliasson's reducibility theory in this regime (our approach actually leads to improvements even in the per-turbative regime: we are able to show, for all energies, " almost reducibility " in some band of analyticity). We also… CONTINUE READING

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