... to hyperbolic basic sets, among other examples. Annals of Mathematics Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents By Marcelo Viana* NONVANISHING ... R.Problem 6. Do almost all Cr,ν cocycles, r + ν > 0 over a hyperbolic ow(ft, à) with local product structure have some nonzero Lyapunov exponents? Analogously, for cocycles over Lorenz-like ... that generic C0 cocycles over general transformations often have vanishing Lyapunov exponents. Evenmore, for Lp cocycles, 1 ≤ p < ∞, the Lyapunov exponents vanish generically,by Arbieto,...