5 research outputs found
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 arbitrary fine resolution and
arbitrary 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
, according to the dependence of the -entropy,
, and of the finite size Lyapunov exponent,
, on .Comment: 24 pages RevTeX, 9 eps figures included, two references added, minor
corrections, one section has been split in two (submitted to PRE
Role of chaos for the validity of statistical mechanics laws: diffusion and conduction
Several years after the pioneering work by Fermi Pasta and Ulam, fundamental
questions about the link between dynamical and statistical properties remain
still open in modern statistical mechanics. Particularly controversial is the
role of deterministic chaos for the validity and consistency of statistical
approaches. This contribution reexamines such a debated issue taking
inspiration from the problem of diffusion and heat conduction in deterministic
systems. Is microscopic chaos a necessary ingredient to observe such
macroscopic phenomena?Comment: Latex, 27 pages, 10 eps-figures. Proceedings of the Conference "FPU
50 years since" Rome 7-8 May 200