Xueting Tian
Published 2015-05-17Version 1
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.
Comments: 23 pages. arXiv admin note: substantial text overlap with arXiv:0808.0350 by other authors; text overlap with arXiv:0905.0739 by other authors
Non-conformal repellers and the continuity of pressure for matrix cocycles
Livsic theorem for matrix cocycles
Matrix cocycles in the learning of dynamical systems
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