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Genericity of trivial Lyapunov spectrum for Lp-cocycles derived from second order linear homogeneous differential equations

Given an ergodic flow $φ^t\colon M\rightarrow M$ defined on a probability space $M$ we study a family of continuous-time kinetic linear cocycles associated to the solutions of the second order linear homogeneous differential equations $\ddot x +α(φ^t(ω))\dot x+β(φ^t(ω))x=0$, where the parameters $α,β$ evolve along the $φ^t$-orbit of $ω\in M$. 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 $L^p$-like topology on the infinitesimal generator, the Lyapunov spectrum is trivial.