大耦合下$C^2$ Cos型拟周期薛定谔余环的Lyapunov指数的精确正则性
The precise regularity of the Lyapunov exponent for $C^2$ Cos-type quasiperiodic Schrödinger cocycles with large couplings
AI总结：
研究大耦合下$C^2$ cos型拟周期薛定谔余环的Lyapunov指数，证明其绝对连续性和$\frac{1}{2}$-Hölder连续性，并刻画谱中局部正则性的精确范围。
摘要：
本文研究了具有$C^2$ cos型势、大耦合常数和固定Diophantine频率的拟周期薛定谔余环的Lyapunov指数的正则性。我们获得了Lyapunov指数的绝对连续性。此外，我们证明了Lyapunov指数是$\frac{1}{2}$-Hölder连续的。进一步地，对于任意给定的$r\in (\frac12, 1)$，我们可以在谱中找到某个能量，使得Lyapunov指数的局部正则性介于$(r-ε)$-Hölder连续性和$(r+ε)$-Hölder连续性之间。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
