Tao, Kai2021-09-292021-09-292020-05-26Tao, K. (2020). Non-perturbative positivity and weak Holder continuity of Lyapunov exponent of analytic quasi-periodic Jacobi cocycles defined on a high dimension torus. <i>Electronic Journal of Differential Equations, 2020</i>(51), pp. 1-14.1072-6691https://hdl.handle.net/10877/14558When 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.Text14 pages1 file (.pdf)enAttribution 4.0 InternationalAnalytic quasi-periodic Jacobi cocyclesHigh dimension torusNon-perturbativePositive Lyapunov exponentWeak Holder continuousArticle