Electron. J. Differential Equations, Vol. 2020 (2020), No. 51, pp. 1-14.

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

Kai Tao

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.

Show me the PDF file (362 KB), TEX file for this article.

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

Return to the EJDE web page