Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations

Bessa, Mário

http://hdl.handle.net/10400.2/13928

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Authors

Bessa, Mário

Abstract(s)

We 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.