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The purpose of these notes is to discuss the advances in the theory ofLyapunov exponents of linear $\text{SL}_2(\mathbb{R})$ cocycles over hyperbolicmaps. The main focus is around results regarding the positivity of the Lyapunovexponent and the regularity of this function with respect to the underlyingdata.

An invitation to $\text{SL}_2(\mathbb{R})$ cocycles over random dynamics