Non-Markovian invariant measures are hyperbolic

Hans Crauel

Stochastic Processes and their Applications, 1993, vol. 45, issue 1, 13-28

Abstract: Suppose [mu] is an invariant measure for a smooth random dynamical system on a d-dimensional Riemannian manifold. We prove that [alpha][mu][less-than-or-equals, slant]dE[mu](max{0,-[lambda][mu]d}), where [alpha][mu] is the relative entropy of [mu], [lambda][mu]d is thesmallest Lyapunov exponent associated with [mu], and E[mu] denotes integration with respect to [mu].

Date: 1993
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