Continuity of Lyapunov exponent for analytic quasi-periodic cocycles on higher-dimensional torus

doi:10.1007/s11464-012-0201-x

Front Math Chin

2012, Vol. 7

Issue (3) : 521-542 https://doi.org/10.1007/s11464-012-0201-x

RESEARCH ARTICLE

Continuity of Lyapunov exponent for analytic quasi-periodic cocycles on higher-dimensional torus

Kai TAO(

)

Department of Mathematics, Nanjing University, Nanjing 210093, China

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Abstract

It is known that the Lyapunov exponent is not continuous at certain points in the space of continuous quasi-periodic cocycles. We show that the Lyapunov exponent is continuous for a higher-dimensional analytic category in this paper. It has a modulus of continuity of the form exp?(-|log?t|σ) for some 0<σ<1.

Keywords Analytic quasi-periodic cocycle Lyapunov exponent continuity large deviation theorem avalanche principle

Corresponding Author(s): TAO Kai,Email:tao.nju@gmail.com

Issue Date: 01 June 2012

Cite this article:

Kai TAO. Continuity of Lyapunov exponent for analytic quasi-periodic cocycles on higher-dimensional torus[J]. Front Math Chin, 2012, 7(3): 521-542.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0201-x
https://academic.hep.com.cn/fmc/EN/Y2012/V7/I3/521

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