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arXiv · 1811.02647

A random cocycle with non H\"older Lyapunov exponent

Pedro Duarte·Silvius Klein·Manuel Santos
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Abstract

We provide an example of a Schr\"odinger cocycle over a mixing Markov shift for which the integrated density of states has a very weak modulus of continuity, close to the log-H\"older lower bound established by W. Craig and B. Simon. This model is based upon a classical example due to Y. Kifer of a random Bernoulli cocycle with zero Lyapunov exponents which is not strongly irreducible. It follows that the Lyapunov exponent of a Bernoulli cocycle near this Kifer example cannot be H\"older or weak-H\"older continuous, thus providing a limitation on the modulus of continuity of the Lyapunov exponent of random cocycles.

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Pedro Duarte, Silvius Klein, Manuel Santos. 2018-11-06. A random cocycle with non H\"older Lyapunov exponent. https://arxiv.org/abs/1811.02647

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