Mathematics department
Southeast University, Jiulonghu Campus
Jiangning District, Nanjing
Jiangsu Province 211189, China
email: ktao@hhu.edu.cn, tao.nju@gmail.com
Kai Tao
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.
DOI: 10.58997/ejde.2020.51
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Kai Tao Mathematics department Southeast University, Jiulonghu Campus Jiangning District, Nanjing Jiangsu Province 211189, China email: ktao@hhu.edu.cn, tao.nju@gmail.com |
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