论文标题
Anosov-katok构造的准周期$ \ mathrm {sl}（2，r）$ cocycles $ cocycles
Anosov-Katok constructions for quasi-periodic $\mathrm{SL}(2,R)$ cocycles
论文作者
论文摘要
我们证明，如果准周期$ \ mathrm {sl}（2，\ r）$ cocycle是二聚体的，那么以下属性在次临界方案中是密集的：对于任何$ \ frac {1} {1} {2} {2} {2} <κ<κ<κ<κ<κ<κ<κ<κ<κ<κ<by，lyapunov Expents均为$ $κ$κ$κ$κ$κ电势的扩展本征具有最佳的亚线性生长。双重操作员关联的亚临界潜力具有幂律衰减本征函数。该证明基于用于准周期性$ \ mathrm {sl}（2，\ r）$ Cocycles的纤维Anosov-katok构造。
We prove that if the frequency of the quasi-periodic $\mathrm{SL}(2,\R)$ cocycle is Diophantine, then the following properties are dense in the subcritical regime: for any $\frac{1}{2}<κ<1$, the Lyapunov exponent is exactly $κ$-Hölder continuous; the extended eigenstates of the potential have optimal sub-linear growth; and the dual operator associated a subcritical potential has power-law decay eigenfunctions. The proof is based on fibered Anosov-Katok constructions for quasi-periodic $\mathrm{SL}(2,\R)$ cocycles.
