Related papers: Statistical-mechanical formulation of Lyapunov exp…

Stochastic dynamical systems are fundamental in state estimation, system identification and control. System models are often provided in continuous time, while a major part of the applied theory is developed for discrete-time systems.…

We compute the full Lyapunov spectra for a hard-disk fluid under temperature gradient and shear. The system is thermalized by deterministic and time-reversible scattering at the boundary. This thermostating mechanism allows for energy…

The stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY-Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent…

We give two kinds of approximation of Lyapunov exponents of rational functions of degree more than one on the projective line over more general fields than that of complex numbers.

Lyapunov exponents of dynamical systems are defined from the rates of divergence of nearby trajectories. For stochastic systems, one typically assumes that these trajectories are generated under the "same noise realization". The purpose of…

Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…

Various kinematical quantities associated with the statistical properties of dynamical systems are examined: statistics of the motion, dynamical bases and Lyapunov exponents. Markov partitons for chaotic systems, without any attempt at…

A cycle expansion for the Lyapunov exponent of a product of random matrices is derived. The formula is non-perturbative and numerically effective, which allows the Lyapunov exponent to be computed to high accuracy. In particular, the free…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

We propose an efficient method to compute Lyapunov exponents and Lyapunov eigenvectors of long-range interacting many-particle systems, whose dynamics is described by the Vlasov equation. We show that an expansion of a distribution function…

We compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact time evolution of tangent-space vectors are derived and are utilized toward…

We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state…

We point out that the Lyapunov exponent of the eigenstate places restrictions on the eigenvalue. Consequently, with regard to non-Hermitian systems, even without any symmetry, the non-conservative Hamiltonians can exhibit real spectra as…

We propose a novel framework to characterize the thermalization of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. We use a classical unitary map model to investigate…

We present a statistical physics framework for description of nonlinear non-equilibrium stochastic processes, modeled via chemical master equation, in the weak-noise limit. Using the Poisson representation approach and applying the…

It is well-known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose an alternative definition of Lyapunov exponent in terms of Lipschitz maps, which are not necessarily differentiable. We show…

Consistent statistical physical description is given for systems where the elementary excitations are composite objects. Explicit calculational scheme is constructed for the energy density and the total number of thermodynamical degrees of…

The deterministic equations describing the dynamics of the atmosphere (and of the climate system) are known to display the property of sensitivity to initial conditions. In the ergodic theory of chaos this property is usually quantified by…

This paper is concerned with relationships of Lyapunov exponents with sensitivity and stability for non-autonomous discrete systems. Some new concepts are introduced for non-autonomous discrete systems, including Lyapunov exponents, strong…

We discuss several numerical methods for calculating Lyapunov exponents (a quantitative measure of chaos) in systems of ordinary differential equations. We pay particular attention to constrained systems, and we introduce a variety of…