  It follows from Oseledec Multiplicative Ergodic Theorem (or Kingman's
Sub-additional 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$\ddot{o}$der continuous cocycles over hyperbolic systems, in this article we
show that either all ergodic measures have same Maximal Lyapunov exponents or
the set of Lyapunov `non-typical' points have full topological entropy and
packing topological entropy. Moreover, we give an estimate of Bowen Hausdorff
entropy from below.
