Simplicity of Lyapunov spectrum for linear cocycles over non-uniformly   hyperbolic systems
  We prove that generic fiber-bunched and H\"older continuous linear cocycles over a non-uniformly hyperbolic system endowed with a u-Gibbs measure have simple Lyapunov spectrum. This gives an affirmative answer to a conjecture proposed by Viana in the context of fiber-bunched cocycles. 
Lucas Backes, Mauricio Poletti, Paulo Varandas and Yuri Lima
math.DS