Global Theory of One-frequency Schr¨odinger Operators I: Stratified Analyticity of the Lyapunov Exponent and the Boundary of Nonuniform Hyperbolicity

@inproceedings{Avila2009GlobalTO,
  title={Global Theory of One-frequency Schr¨odinger Operators I: Stratified Analyticity of the Lyapunov Exponent and the Boundary of Nonuniform Hyperbolicity},
  author={Artur Avila},
  year={2009}
}
We study Schrödinger operators with a one-frequency analytic potential, focusing on the transition between the two distinct local regimes characteristic respectively of large and small potentials. From the dynamical point of view, the transition signals the emergence of nonuniform hyperbolicity, so the dependence of the Lyapunov exponent with respect to… CONTINUE READING