UNIFORM LYAPUNOV EXPONENTS ARE REALISED BY ERGODIC INVARIANT MEASURES

Abstract

Given a differentiable random dynamical system on a finite-dimensional differentiable manifold with a compact random invariant set, we show that there exists an ergodic invariant measure, supported by the invariant set, such that the leading Lyapunov exponent associated with this invariant measure equals the uniform Lyapunov exponent with respect to the invariant set. This is extended to sums of Lyapunov exponents and to the Lyapunov dimension of the set.