Abstract
We consider a probability space M on which an ergodic flow φt:M→M is defined. We study a family of continuous-time linear cocycles, referred to as kinetic, that are associated with solutions of the second-order linear homogeneous differential equation x¨+α(φt(ω))x˙+β(φt(ω))x=0. Here, the parameters α and β evolve along the φt-orbit of ω∈M. Our main result states that for a generic subset of kinetic continuous-time linear cocycles, where generic means a Baire second category with respect to an Lp-like topology on the infinitesimal generator, the Lyapunov spectrum is trivial.
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