Related papers: Spatiotemporal chaos: the microscopic perspective
The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time…
Using dynamical systems methods, we describe the evolution of a minimally coupled scalar field and a Friedmann-Lemaitre-Robertson-Walker universe in the context of general relativity, which is relevant for inflation and late-time…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
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 chaos in stellar systems is studied using the theory of dynamical systems and the Van Kampen stochastic differential equation approach. The exponential instability (chaos) of spherical N-body gravitating systems, already known…
Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner.…
We study the probability densities of finite-time or \local Lyapunov exponents (LLEs) in low-dimensional chaotic systems. While the multifractal formalism describes how these densities behave in the asymptotic or long-time limit, there are…
We present a review of our recent work in extending the successful dynamical mean-field theory from the equilibrium case to nonequilibrium cases. In particular, we focus on the problem of turning on a spatially uniform, but possibly time…
By interpreting a temporal network as a trajectory of a latent graph dynamical system, we introduce the concept of dynamical instability of a temporal network, and construct a measure to estimate the network Maximum Lyapunov Exponent (nMLE)…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
We calculate the Lyapunov exponents describing spatial clustering of particles advected in one- and two-dimensional random velocity fields at finite Kubo numbers Ku (a dimensionless parameter characterising the correlation time of the…
We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of…
The dynamics of the Mixmaster Universe is analized in a covariant picture via Misner--Chitre-like variables for an ADM Hamiltonian approach. The system outcomes as isomorphic to a billiard on the Lobachevsky plane and Lyapunov exponents are…
As a new tool to describe the behaviour of a dynamical system, we introduce the concept of "covariant Lyapunov field", i.e. a field which assigns all the components of covariant Lyapunov vectors at almost all points of the phase space. We…
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the…
The dissipation associated with nonequilibrium flow processes is reflected by the formation of strange attractor distributions in phase space. The information dimension of these attractors is less than that of the equilibrium phase space,…
In this work, we investigate scale invariance in the temporal evolution and chaotic regime of discrete dynamical systems. By exploiting the close interrelation between scaling and inversion transformations, we formulate scale symmetry in…
By analyzing chaotic states of the one-dimensional Kuramoto-Sivashinsky equation for system sizes L in the range 79 <= L <= 93, we show that the Lyapunov fractal dimension D scales microextensively, increasing linearly with L even for…
We review and complete the existing literature on the kinetic theory of spatially homogeneous systems with long-range interactions taking collective effects into account. The evolution of the system as a whole is described by the…
Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…