Browsing by Author "Amaro, Dinis"
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- Genericity of trivial Lyapunov spectrum for L-cocycles derived from second order linear homogeneous differential equationsPublication . Amaro, Dinis; Bessa, Mário; Vilarinho, HelderWe consider a probability space M on which an ergodic flow 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 . 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 -like topology on the infinitesimal generator, the Lyapunov spectrum is trivial.
- Simple Lyapunov spectrum for linear homogeneous differential equations with Lp parametersPublication . Amaro, Dinis; Bessa, Mário; Vilarinho, HelderIn the present paper we prove that densely, with respect to an Lp-like topology, the Lyapunov exponents associated to linear continuous-time cocycles induced by second order linear homogeneous differential equations are almost everywhere distinct. The coefficients evolve along the orbit for an ergodic flow defined on a probability space. We also obtain the corresponding version for the frictionless equation and for a Schrödinger equation.