Dynamical entropy for systems with stochastic perturbation

Dynamics of deterministic systems perturbed by random additive noise is cha racterized quantitatively, Since for such systems the Kolmogorov-Sinai (KS) entropy diverges if the diameter of the partition tends to zero, we analyz e the difference between the total entropy of a noisy system and the entrop y of the noise itself. We show that this quantity is finite and non-negativ e and we call it the dynamical entropy of the noisy system. In the weak noi se limit this quantity is conjectured to tend to the KS entropy of the dete rministic system. In particular, we consider one-dimensional systems with n oise described by a finite-dimensional kernel for which the Frobenius-Perro n operator can be represented by a finite matrix.