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arXiv · 1601.06118

Singular analytic linear cocycles with negative infinite Lyapunov exponents

Christian Sadel·Disheng Xu
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Abstract

We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form. As a consequence, an arbitrarily small analytic perturbation leads to distinct Lyapunov exponents. Moreover, in the one-frequency case where the $k$-th Lyapunov exponent is finite and the $k+1$st negative infinite, we obtain a simple criterion for domination in which case there is a splitting into a nilpotent part and an invertible part.

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Christian Sadel, Disheng Xu. 2017-03-21. Singular analytic linear cocycles with negative infinite Lyapunov exponents. https://doi.org/10.1017/etds.2017.52

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