Related papers: Pesin-Type Identity for Weak Chaos
We investigate ergodic-theoretical quantities and large deviation properties of one-dimensional intermittent maps, that have not only an indifferent fixed point but also a singular structure such that the uniform measure is invariant under…
We consider an elastic manifold of internal dimension $d$ and length $L$ pinned in a $N$ dimensional random potential and confined by an additional parabolic potential of curvature $\mu$. We are interested in the mean spectral density…
Ultrametric concepts are applied to the Bernoulli map, showing the adequateness of the non-Archimedean metrics to describe in a simple and direct way the chaotic properties of this map. Lyapunov exponent and Kolmogorov entropy appear to…
We generalize the concept of convective (or velocity-dependent) Lyapunov exponent $\Lambda(v)$ to an entire spectrum $\Lambda(v,n)$. Our results are supported by the consistency between the outcome of the chronotopic approach [{\it S. Lepri…
Nonequilibrium steady state (NESS) is a quasistationary state, in which exist currents that continuously produce entropy, but the local observables are stationary everywhere. We propose a theory of NESS under the framework of quantum chaos.…
We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions $\rho(p,q)$. Of particular interest is $\lambda_2$, an exponent which quantifies the rate at which chaotically evolving…
We present extensive numerical investigations on the ergodic properties of two identical Pomeau-Manneville maps interacting on the unit square through a diffusive linear coupling. The system exhibits anomalous statistics, as expected, but…
We study the evolution of the probability density of ensembles of iterates of the logistic map that advance towards and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable…
The Lyapunov exponents and the KS entropy for a two dimensional Lorentz gas at low densities are defined for general non-equilibrium states and calculated with the use of a Lorentz-Boltzmann type equation. In equilibrium the density…
The coupled entropy, $H_\kappa,$ is proven to uniquely satisfy the requirement that a generalized entropy be a measure of the uncertainty at the scale, $\sigma,$ for a class of non-exponential distributions. The coupled stretched…
We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…
Ergodic parameters like the Lyapunov and the conditional exponents are global functions of the invariant measure, but the invariant measure itself contains more information. A more complete characterization of the dynamics by new families…
The present work analyzes the statistics of finite scale local Lyapunov exponents of pairs of fluid particles trajectories in fully developed incompressible homogeneous isotropic turbulence. According to the hypothesis of fully developed…
A phenomenon of weak transient chaos is discussed that is caused by sub-exponential divergence of trajectories in the basin of a non-chaotic attractor. Such a regime is not easy to detect, because conventional characteristics, such as the…
A simple Kronig-Penney model for one-dimensional (1D) mesoscopic systems with $\delta $ peak potentials is used to study numerically the influence of a spatial disorder on the conductance fluctuations and distribution at different regimes.…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
In chaotic dynamical systems, an infinitesimal perturbation is exponentially amplified at a time-rate given by the inverse of the maximum Lyapunov exponent $\lambda$. In fully developed turbulence, $\lambda$ grows as a power of the Reynolds…
In search for mathematically tractable models of anomalous diffusion, we introduce a simple dynamical system consisting of a chain of coupled maps of the interval whose Lyapunov exponents vanish everywhere. The volume preserving property…
The aim of this paper is to show how extracting dynamical behavior and ergodic properties from deterministic chaos with the assistance of exact invariant measures. On the one hand, we provide an approach to deal with the inverse problem of…
Entanglement entropy is a powerful tool in characterizing universal features in quantum many-body systems. In quantum chaotic Hermitian systems, typical eigenstates have near maximal entanglement with very small fluctuations. Here, we show…