Related papers: Large deviations of Lyapunov exponents
The largest Lyapunov exponent of an ergodic Hamiltonian system is the rate of exponential growth of the norm of a typical vector in the tangent space. For an N-particle Hamiltonian system, with a smooth Hamiltonian of the type p^2 + v(q),…
Finite-time Lyapunov exponents of generic chaotic dynamical systems fluctuate in time. These fluctuations are due to the different degree of stability across the accessible phase-space. A recent numerical study of spatially-extended systems…
We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes…
The Lyapunov exponents of a dynamical system measure the average rate of exponential stretching along an orbit. Positive exponents are often taken as a defining characteristic of chaotic dynamics. However, the standard…
We calculate the spectrum of Lyapunov exponents for a point particle moving in a random array of fixed hard disk or hard sphere scatterers, i.e. the disordered Lorentz gas, in a generic nonequilibrium situation. In a large system which is…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
Lyapunov exponents (LEs) are key indicators of chaos in dynamical systems. In general relativity the classical definition of LE meets difficulty because it is not coordinate invariant and spacetime coordinates lose their physical meaning as…
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…
This paper investigates the behaviour of open billiard systems in high-dimensional spaces. Specifically, we estimate the largest Lyapunov exponent, which quantifies the rate of divergence between nearby trajectories in a dynamical system.…
Important information about the dynamical structure of a differential system can be revealed by looking into its invariant compact manifolds, such as equilibria, periodic orbits, and invariant tori. This knowledge is significantly increased…
The tangent dynamics of the Lyapunov modes and their dynamics as generated numerically - {\it the numerical dynamics} - is considered. We present a new phenomenological description of the numerical dynamical structure that accurately…
Cross-sectional observations from a dynamical system can be modeled via steady-state distributions of Markov processes. The major challenge is then to determine whether the process parameters can be identified and estimated from the…
New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…
Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…
The Lagrangian derivatives of finite-time Lyapunov exponents and the corresponding characteristic directions are shown to satisfy time-asymptotic differential constraints in chaotic flows. The constraints are valid for any metric tensor,…
A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random $N\times N$ matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
In the dynamical systems approach to describing turbulent or otherwise chaotic flows, an important quantity is the Lyapunov exponents and vectors that characterize the strange attractor of the flow. In particular, knowledge of the Lyapunov…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…
The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with…