Abstract
Suppose μ is an invariant measure for a smooth random dynamical system on a d-dimensional Riemannian manifold. We prove that α μ ⩽ dE μ (max{0,− λ μ d }), where α μ is the relative entropy of μ, λ μ d is thesmallest Lyapunov exponent associated with μ, and E μ denotes integration with respect to μ.
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