The transition from deterministic chaos to a stochastic process

Deterministic dynamical systems of Langevin type recently introduced by Beck and Roepsdorf (Physica A 145 (1987) 1) generate Langevin dynamics in a suitable limit. We discuss the transition from chaos to randomness in these systems under the point of view of the attractor dimension and dynamical entropy and show that the limit of a stochastic process is reached via a shift of the deterministic properties towards the infinitesimal length scales.