Bessa, MárioVilarinho, Helder2023-05-252023-05-252014M. Bessa, H. Vilarinho, Fine properties of Lp-cocycles which allow abundance of simple and trivial spectrum, 256, 7, 2337-2367, 20140022-0396http://hdl.handle.net/10400.2/13842In this paper we prove that the class of accessible and saddle-conservative cocycles (a wide class which includes cocycles evolving in GL(d,R), SL(d,R) and Sp(d,R)) Lp-densely have a simple spectrum. We also prove that for an Lp-residual subset of accessible cocycles we have a one-point spectrum. Finally, we show that the linear differential system versions of previous results also hold and give some applications.engLinear cocyclesLinear differential systemsMultiplicative ergodic theoremLyapunov exponentsjournal article10.1016/j.jde.2014.01.003