0 Chaos or Noise — Difficulties of a Distinction

In experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrarily fine resolution and arbitrarily high embedding dimension. These restrictions limit our ability to distinguish between signals generated by different systems, such as regular, chaotic or stochastic ones, when analyzed from a time series point of view. We propose to classify the signal behavior, without referring to any specific model, as stochastic or deterministic on a certain scale of the resolution ǫ, according to the dependence of the (ǫ, τ)-entropy, h(ǫ, τ), and of the finite size Lyapunov exponent, λ(ǫ), on ǫ.