We report the results of studies of nonlinear dynamics and dynamical chaos in Hamiltonian systems composed of many interacting particles. The importance of the Lyapunov exponents and the Kolmogorov-Sinai entropy is discussed in the context of ergodic theory and nonequilibrium statistical mechanics. Two types of systems are studied: hard-ball models for the motion of a tracer or Brownian particl...

It is known that unstable periodic orbits of a given map give information about the natural measure of a chaotic attractor. In this work we show how these orbits can be used to calculate the density function of the first Poincaré returns. The close relation between periodic orbits and the Poincaré returns allows for analytical and semi-analytical estimations of relevant quantities in dynamical ...

The chaotic scattering theory is here extended to obtain escape-rate expressions for the transport coefficients appropriate for a simple classical fluid, or for a chemically reacting system. This theory allows various transport coefficients such as the coefficients of viscosity, thermal conductivity, etc., to be expressed in terms of the positive Lyapunov exponents and Kolmogorov-Sinai entropy ...

Abstract The quark-gluon plasma is written by the non-Abelian gauge theory. dynamics of SU(2) are given Hamiltonian function, which contains quadratic part field strength tensor F μ v a {\rm{F}}_{\mu v}^{\rm{...

The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is ...

We study the quantization of two examples of classically chaotic dynamics, the Anosov dynamics of “cat maps” on a two dimensional torus, and the dynamics of baker’s maps. Each of these dynamics is implemented as a discrete group of automorphisms of a von Neumann algebra of functions on a quantized torus. We compute the non-commutative generalization of the Kolmogorov-Sinai entropy, namely the C...

BACKGROUND Evaluations of electric power distribution network risks must address the problems of incomplete information and changing dynamics. A risk evaluation framework should be adaptable to a specific situation and an evolving understanding of risk. METHODS This study investigates the use of symbolic dynamics to abstract raw data. After introducing symbolic dynamics operators, Kolmogorov-...

Pesin's identity provides a profound connection between the Kolmogorov-Sinai entropy h_{KS} and the Lyapunov exponent lambda. It is well known that many systems exhibit subexponential separation of nearby trajectories and then lambda=0. In many cases such systems are nonergodic and do not obey usual statistical mechanics. Here we investigate the nonergodic phase of the Pomeau-Manneville map whe...

It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be mod-eled as classical systems of particles interacting with short range, repulsive forces. Here we give a brief introduction to those parts of chaos theory that are relevant for understanding some features of non-equilibrium processes in fluids. We introduce the n...

We make use of a wavelet method to extract, from experimental velocity signals obtained in an evolutive flow, the dominating velocity components generated by vortex dynamics. We characterize the resulting time series complexity by means of a joint use of data compression and of an entropy diffusion method. We assess that the time series emerging from the wavelet analysis of the vortex dynamics ...