Non-perturbative positivity and weak Holder continuity of Lyapunov exponent of analytic quasi-periodic Jacobi cocycles defined on a high dimension torus

• Main Author: Kai Tao
• Format: Article
• Language: English
• Published: Texas State University 2020-05-01
• Series: Electronic Journal of Differential Equations
• Subjects: analytic quasi-periodic jacobi cocycles; high dimension torus; non-perturbative; positive lyapunov exponent; weak holder continuous
• Online Access: http://ejde.math.txstate.edu/Volumes/2020/51/abstr.html

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.