We consider the quasi-periodic cocycles with Diophantine. Let be a normed space endowed with the matrix norm, whose elements are the matrices. Assume that is jointly continuous, depends analytically on and is Holder continuous in , where is a compact metric space and is the torus. We prove that if two Lyapunov exponents are distinct at one point , then these two Lyapunov exponents are Holder continuous at any E in a ball central at . Moreover, we will give the expressions of the radius of this ball and the Holder exponents of the two Lyapunov exponents.
Submitted October 10, 2014. Published March 20, 2015.
Math Subject Classifications: 37C55, 37F10.
Key Words: Lyapunov exponent; quasiperodic cocycles; Holder exponent.
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| Kai Tao |
College of Sciences, Hohai University
1 Xikang Road
Nanjing, Jiangsu 210098, China
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