References

In this talk I will discuss the prevalence of exponential behavior (non-zero Lyapunov exponents) for linear cocycles over partially hyperbolic maps. The main result may be seen as an extension of a classical Theorem of Fursten-berg for random matrices [3], as well of recent results for deterministic prod-ucts of matrices. In the determinist setting J. Bochi and M. Viana [1] have shown the abundance of zero Lyapunov exponents for continuous linear cocycles over an ergodic invertible measurable transformation. On the other hand, C. Bonatti and M. Viana [2] proved the prevalence of non-zero Lyapunov ex-ponents for dominated Hölder continuous linear cocycles over a uniformly hyperbolic diffeomorphism. Recently, M. Viana [4] has not only removed the domination assumption, but extended the result over a non-uniformly hyperbolic base. This is a joint work with A. Avila and M. Viana