Bessa, Mário2023-05-312023-05-312023Bessa, M. Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations. Aequat. Math. 97, 467–487 (2023)0001-9054http://hdl.handle.net/10400.2/13928We consider 3×3 partially hyperbolic linear differential systems over an ergodic flow X^t and derived from the linear homogeneous differential equation x''(t)+β(X^t(t))x'(t)+ γ(t)x(t) = 0. Assuming that the partial hyperbolic decomposition E^s ⊕ E^c ⊕ E^u is proper and displays a zero Lyapunov exponent along the central direction E^c we prove that some C^0 perturbation of the parameters β(t) and γ(t) can be done in order to obtain non-zero Lyapunov exponents and so a chaotic behaviour of the solution.engLyapunov exponentsJerk equationsPartial hyperbolicityjournal article10.1007/s00010-023-00948-z