Different aspects of the predictability problem in dynamical systems are reviewed. The deep
relation among Lyapunov exponents, Kolmogorov–Sinai entropy, Shannon entropy and …

The title of this book already says something about its contents and historical origin, but
since it is meant in a rigorous mathematical context, a few words of explanation may be …

One century after Einstein's work, Brownian motion still remains both a fundamental open
issue and a continuous source of inspiration for many areas of natural sciences. We first …

Deterministic chaos has been implicated in numerous natural and man-made complex
phenomena ranging from quantum to astronomical scales and in disciplines as diverse as …

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 …

A valuable introduction for newcomers as well as an important reference and source of
inspiration for established researchers, this book provides an up-to-date summary of central …

We study anomalous heat conduction and anomalous diffusion in low-dimensional systems
ranging from nonlinear lattices, single walled carbon nanotubes, to billiard gas channels …

We show that macroscopic nonintegrable lattices of spins 1/2, which are often considered to
be chaotic, do not exhibit the basic property of classical chaotic systems, namely …

Brownian motion is a dynamic behavior with random changes over time (stochastic) that
occurs in many vital functions related to fluid environments, stock behavior, or even …

We demonstrate that a completely integrable classical mechanical model, namely the lattice
Landau-Lifshitz classical spin chain, supports diffusive spin transport with a finite diffusion …