Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 51, pp. 1-14.

Title: Non-perturbative positivity and weak Holder continuity of
       Lyapunov exponent of analytic quasi-periodic Jacobi cocycles defined 
       on a high dimension torus
       
Author: Kai Tao (Southeast Univ., Jiulonghu, Nanjing, China)

Abstract:
 When analytic quasi-periodic cocycles are defined on a high dimension torus,
 their Lyapunov exponents have perturbative positivity and continuity.
 In this article, we study a class of analytic quasi-periodic Jacobi cocycles
 defined on a two dimension torus. We show that in the non-perturbative large 
 coupling regimes, the Lyapunov exponent is positive for any frequency and 
 weak Holder continuous for the full-measured frequency.
 
Submitted January 4, 2020. Published May 26, 2020.
Math Subject Classifications: 37C55, 37F10.
Key Words: Analytic quasi-periodic Jacobi cocycles; high dimension torus;
           non-perturbative; positive Lyapunov exponent; weak Holder continuous.