中科院数学与系统科学研究院
数学研究所
学术报告
动力系统研讨班
报告人：张正鹤 (加利福尼亚大学 河滨分校）
题 目：Positivity and large deviations of the Lyapunov exponents for potentials generated by hyperbolic transformations
时 间：2023.06.23（星期五）16:00-17:00
地 点：数学院南楼N602
摘 要：In this talk, I will introduce some recent joint work with A. Avila and D. Damanik in showing positivity and large deviations of the Lyapunov exponent for Schrodinger operators with potentials generated by hyperbolic transformations. Specifically, we consider the base dynamics which is a subshift of finite type with an ergodic measure admitting a bounded distortion property and which has a fixed point. We show that if the potentials are locally constant or globally fiber bunched, then the set of zero Lyapunov exponent is finite. Moreover, we have a uniform large deviation estimate away from this finite set. As a consequence, we obtain full spectral Anderson localization for such potentials.
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