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- W2971144586 abstract "We derive large deviations type (LDT) estimates for linear cocycles over an ergodic multifrequency torus translation. These models are called quasi-periodic cocycles. We make the following assumptions on the model: the translation vector satisfies a generic Diophantine condition, and the fiber action is given by a matrix valued analytic function of several variables which is not identically singular. The LDT estimates obtained here depend on some uniform measurements on the cocycle. Our general results derived in [9] regarding the continuity properties of the Lyapunov exponents (LE) and of the Oseledets filtration and decompositions are then applicable, and we obtain local weak-Holder continuity of these quantities in the presence of gaps in the Lyapunov spectrum. The main new feature of this work is allowing a cocycle depending on several variables to have singularities, i.e. points of non invertibility. This requires a careful analysis of the set of zeros of certain analytic functions of several variables and of the singularities (i.e. negative infinity values) of pluri-subharmonic functions related to the iterates of the cocycle. A refinement of this method in the one variable case leads to a stronger LDT estimate and in turn to a stronger, nearly-Holder modulus of continuity of the LE, Oseledets filtration and Oseledets decomposition. This is a draft of a chapter in our forthcoming research monograph [9]." @default.
- W2971144586 created "2019-09-05" @default.
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- W2971144586 date "2014-10-03" @default.
- W2971144586 modified "2023-09-26" @default.
- W2971144586 title "Lyapunov exponents of analytic cocycles with singularities" @default.
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