Abstract by Xue Liu
Random exponential dichotomies, the random shadowing lemma and applications
In this paper, we conisder general C^2 random dynamical system on Riemannian manifold. We define random hyperbolic set for a random dynamical system by using random exponential dichotomy. After introducing the point in the graph sense, we can prove a kind of random shadowing lemma which is different with the previous work. Under some specific condition, we also can prove there exists a strong full random horseshoe nearby a orbits of a random homoclinic points that is also a random version of the Birkhoff-smale theorem.