Special Session 89: DYNAMICS AND SPECTRA OF QUASIPERIODIC SCHRODINGER OPERATORS
Absolute continuity and Holder continuity of the integrated density of states (IDS) for the analytic quasiperiodic Schrodinger operators
Jing Wang
Nanjing University of Science and Technology
Peoples Rep of China
Co-Author(s):    Xu Xu, Jiangong You, Qi Zhou
Abstract:
In this talk, we will consider the continuity of the IDS for analytic quasiperiodic Schrodinger operators. In the subcritical region, we prove that the IDS and Lyapunov exponents are log-Holder continuous for operators with Liouvillean frequency; in the supercritical region, we prove that the IDS is absolutely continuous for operators with trigonometric potential and Diophantine frequency. The main tool is quantitative almost reducibility and Aubry duality. This talk is based on joint works with Xu Xu, Qi Zhou and Jiangong You.
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