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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer Berlin Heidelberg

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DOI

10.1016/0304-3886(82)90091-2

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1432-0916

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Continuity of the Lyapunov Exponents for Quasiperi

Authors: Pedro Duarte Silvius Klein
Publish Date: 2014/05/11
Volume: 332, Issue: 3, Pages: 1113-1166
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Abstract

Consider the Banach manifold of real analytic linear cocycles with values in the general linear group of any dimension and base dynamics given by a Diophantine translation on the circle We prove a precise higher dimensional Avalanche Principle and use it in an inductive scheme to show that the Lyapunov spectrum blocks associated to a gap pattern in the Lyapunov spectrum of such a cocycle are locally Hölder continuous Moreover we show that all Lyapunov exponents are continuous everywhere in this Banach manifold irrespective of any gap pattern in their spectra These results also hold for Diophantine translations on higher dimensional tori albeit with a loss in the modulus of continuity of the Lyapunov spectrum blocks

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