S.N. Chow and E.S. Van Vleck,

``A Shadowing Lemma for Random Diffeomorphisms,''

(1992) Random & Computational Dynamics 1(2) pp. 197-218.

ABSTRACT

Using a Multiplicative Ergodic Theorem for random diffeomorphisms on a
a compact Reimannian manifold we define a type of hyperbolicity and using
exponential dichotomy we state and prove a shadowing lemma for random
diffeomorphisms. Our result holds for almost all initial conditions and almost
all infinite sequences of diffeomorphisms. The value of the shadowing
distance, $\epsilon$, is uniform with respect to the local error, $\delta$. We
apply our results to iterated function systems.