Anosov-Katok Constructions for Quasi-Periodic SL(2,R)Cocycles  

作　　者：Nikolaos Karaliolios Xu Xu Qi Zhou 

机构地区：[1]Universitéde Lille,Lille,France [2]Department of Mathematics,Nanjing University,Nanjing 210093,China [3]Chern Institute of Mathematics and LPMC,Nankai University,Tianjin 300071,China

出　　处：《Peking Mathematical Journal》2024年第1期203-245,共43页北京数学杂志（英文）

基　　金：N.Karaliolios was partially supported by LABEX CEMPI(ANR-11-LABX-0007-01)while a post-doc at Université de Lille;.Q.Zhou was partially supported by National Key R&D Program of China(No.2020YFA0713300);NSFC(Grant No.12071232);The Science Fund for Distinguished Young Scholars of Tianjin(No.19JCJQJC61300);Nankai Zhide Foundation。

摘　　要：We prove that if the frequency of the quasi-periodic SL(2,R)cocycle is Diophantine,then each of the following properties is dense in the subcritical regime:for any 1/2<κ<1,the Lyapunov exponent is exactlyκ-Hölder continuous;the extended eigenstates of the potential have optimal sub-linear growth;and the dual operator associated with a subcritical potential has power-law decaying eigenfunctions.The proof is based on fibered Anosov-Katok constructions for quasi-periodic SL(2,R)cocycles.

关 键 词：QUASI-PERIODIC Anosov-Katok construction Almost-reducibility 

分 类 号：O17[理学—数学]