Related papers: Instability statistics and mixing rates
In this Letter we show that the analysis of Lyapunov-exponents fluctuations contributes to deepen our understanding of high-dimensional chaos. This is achieved by introducing a Gaussian approximation for the large deviation function that…
Lyapunov exponents measure the average exponential growth rate of typical linear perturbations in a chaotic system, and the inverse of the largest exponent is a measure of the time horizon over which the evolution of the system can be…
The phase space trajectories of many body systems charateristic of simple fluids are highly unstable. We quantify this instability by a set of Lyapunov exponents, which are the rates of exponential divergence, or convergence, of initial…
Reactivity, contractivity, and Lyapunov exponents are powerful tools for studying the stability properties of dynamical systems and have been extensively investigated in the literature for decades. In this paper, we review and extend the…
Some 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 how a…
The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with…
Generic dynamical systems have `typical' Lyapunov exponents, measuring the sensitivity to small perturbations of almost all trajectories. A generic system has also trajectories with exceptional values of the exponents, corresponding to…
We study asymptotic stability of continuous-time systems with mode-dependent guaranteed dwell time. These systems are reformulated as special cases of a general class of mixed (discrete-continuous) linear switching systems on graphs, in…
We consider low--dimensional dynamical systems with a mixed phase space and discuss the typical appearance of slow, polynomial decay of correlations: in particular we emphasize how this mixing rate is related to large deviations properties.
For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the…
In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov…
We investigate the dependence of Poincar\'e recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct…
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values…
Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corresponding quantities, that is, Lyapunov exponents and…
General theoretic approach to classical Loschmidt echoes in chaotic systems with many degrees of freedom is developed. For perturbations which affect essentially all degrees of freedom we find a doubly exponential decay with the rate…
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of…
The Lyapunov exponent is used to characterize the stability of the dynamic response of the system, and it is often employed to verify if a system is chaotic. Since its discovery in the nineteenth century, various methods have been proposed…
In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…
We investigate functions that are exact solutions to chaotic dynamical systems. A generalization of these functions can produce truly random numbers. For the first time, we present solutions to random maps. This allows us to check,…
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…