The arithmetic version of the frequency transition conjecture for the almost Mathieu operators was recently proved by Jitomirskaya and Liu[34].We give a new proof via reducibility theory and duality,which derives from...The arithmetic version of the frequency transition conjecture for the almost Mathieu operators was recently proved by Jitomirskaya and Liu[34].We give a new proof via reducibility theory and duality,which derives from the method developed in[22](in fact it is a simplified version).This new proof is applicable to more general quasiperiodic operators.展开更多
In this paper,we give an asymptotic estimate for the entropy,i.e.,the sum of all positive Lyapunov exponents,of the quasi-periodic nite-range operator with a large trigonometric polynomial potential and Diophantine fr...In this paper,we give an asymptotic estimate for the entropy,i.e.,the sum of all positive Lyapunov exponents,of the quasi-periodic nite-range operator with a large trigonometric polynomial potential and Diophantine frequency.展开更多
基金supported by National Key R&D Program of China(No.2020YFA0713300)and NSFC(No.11871286)supported by NSF DMS-1901462.L.Ge was partially supported by AMS-Simons Travel Grant 2020-2022supported by China Scholarship Council(No.201906190072)and NSFC(No.11771205).
文摘The arithmetic version of the frequency transition conjecture for the almost Mathieu operators was recently proved by Jitomirskaya and Liu[34].We give a new proof via reducibility theory and duality,which derives from the method developed in[22](in fact it is a simplified version).This new proof is applicable to more general quasiperiodic operators.
基金The second author was supported by National Natural Science Foundation of China(Grant No.11871286).
文摘In this paper,we give an asymptotic estimate for the entropy,i.e.,the sum of all positive Lyapunov exponents,of the quasi-periodic nite-range operator with a large trigonometric polynomial potential and Diophantine frequency.
