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

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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