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

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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(−∣logt∣σ) for some 0 < σ < 1.

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  1. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Kai Tao

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  1. Kai Tao
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Correspondence to Kai Tao.

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Tao, K. Continuity of Lyapunov exponent for analytic quasi-periodic cocycles on higher-dimensional torus. Front. Math. China 7, 521–542 (2012). https://doi.org/10.1007/s11464-012-0201-x

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  • DOI: https://doi.org/10.1007/s11464-012-0201-x

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