论文标题
$ c^2 $ cos-type quasiperiodicschrödingercocycles与大耦合的确切规律性
The precise regularity of the Lyapunov exponent for $C^2$ Cos-type quasiperiodic Schrödinger cocycles with large couplings
论文作者
论文摘要
在本文中，我们研究了具有$ c^2 $ cos-type电位，大耦合常数和固定的双苯胺频率的ic酸schrödingercocycles lyapunov指数的规律性。我们获得Lyapunov指数的绝对连续性。此外，我们证明Lyapunov指数为$ \ frac {1} {2} $ - Hölder连续。此外，对于（\ frac12，1）$中的任何给定的$ r \，我们可以在频谱中找到一些能量，其中Lyapunov指数的本地规律性在$（R-ε）$-Hölder连续性和$（R+ε）$-Hölder连续性之间。
In this paper, we study the regularity of the Lyapunov exponent for quasiperiodic Schrödinger cocycles with $C^2$ cos-type potentials, large coupling constants, and a fixed Diophantine frequency. We obtain the absolute continuity of the Lyapunov exponent. Moreover, we prove the Lyapunov exponent is $\frac{1}{2}$-Hölder continuous. Furthermore, for any given $r\in (\frac12, 1)$, we can find some energy in the spectrum where the local regularity of the Lyapunov exponent is between $(r-ε)$-Hölder continuity and $(r+ε)$-Hölder continuity.
