On Recurrent Cocycles and the Non-existence of Random Xed Points
نویسندگان
چکیده
This paper deals with cocycles over ergodic metric dynamical systems with values in the semi-direct product of Z 2 and R. We show that such cocycles are recurrent under very general assumptions. Furthermore, we give criteria for the existence of invariant measures for group valued cocycles. With that, examples of continuous random dynamical systems on a compact interval without random xed points are constructed. This shows that it is impossible to generalize topological xed point theorems to the case of random dynamical systems.
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