摘 要：It follows from Oseledec Multiplicative Ergodic Theorem (or Kingman’s sub-additive Ergodic Theorem) that the set of ‘non-typical’ points for which the Oseledec averages of a given continuous cocycle diverge has zero measure with respect to any invariant probability measure. In strong contrast, for any H¨older continuous cocycles over hyperbolic systems, in this talk we show that either all ergodic measures have same Maximal Lyapunov exponents or the set of Lyapunov ‘non-typical’ points is a dense $G_delta$ subset and carries full topological entropy and packing topological entropy. Moreover, we give an estimate of Bowen Hausdorff entropy from below by the metric entropy of ergodic measures which are not Lyapunov minimizing, and if further the function of integrable Lyapunov exponent is lower semi-continuous with respect to invariant measures, the set of Lyapunov ‘non-typical’ points carries full Bowen Hausdorff entropy.
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