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。
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 co...
This paper focuses on the reducibility of two-dimensional almost periodic system with small perturbation. We use the KAM iterative method to get the reducibility by an almost periodic transformation. The system has be...
supported by National Nature Science Foundation of China grant(No.71774070)。
In the present paper,we prove the 1/2-Holder continuity of spectral measures for the C^k Schrodinger operators.This result is based on the quantitative almost reducibility and an estimate for the growth of the Schrodi...
The NSF(11571327) of China;NSF(ZR2013AM026) of Shandong Province
In this paper, we use KAM methods to prove that there are positive measure Cantor sets such that for small perturbation parameters in these Cantor sets a class of almost periodic linear differential equations are redu...