We present an investigation of epsilon -entropy, h(epsilon), in dynamical s
ystems, stochastic processes and turbulence, This tool allows for a suitabl
e characterization of dynamical behaviours arising in systems with many dif
ferent scales of motion. Particular emphasis is put on a recently proposed
approach to the calculation of the epsilon -entropy based on the exit-time
statistics. The advantages of this method are demonstrated in examples of d
eterministic diffusive maps, intermittent maps, stochastic self- and multi-
affine signals and experimental turbulent data. Concerning turbulence, the
multifractal formalism applied to the exit-time statistics allows us to pre
dict that h(epsilon) similar to epsilon (-3) for velocity-time measurement.
This power law is independent of the presence of intermittency and has bee
n confirmed by the experimental data analysis. Moreover, we show that the e
psilon -entropy density of a three-dimensional velocity field is affected b
y the correlations induced by the sweeping of large scales. (C) 2000 Elsevi
er Science B.V. All rights reserved.