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

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.

Keywords

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

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