Đề tài " Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents "

We prove that for any s 0 the majority of C s linear cocycles over any hyperbolic (uniformly or not) ergodic transformation exhibit some nonzero Lyapunov exponent: this is true for an open dense subset of cocycles and, actually, vanishing Lyapunov exponents correspond to codimension-∞. This open dense subset is described in terms of a geometric condition involving the behavior of the cocycle over certain heteroclinic orbits of the transformation.

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2    8    1    24-07-2021