Related papers: Maximally Chaotic Dynamical System of Infinite Dim…
For general dissipative dynamical systems we study what fraction of solutions exhibit chaotic behavior depending on the dimensionality $d$ of the phase space. We find that a system of $d$ globally coupled ODE's with quadratic and cubic…
We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on…
Hyperbolic flows, as formulated by Anosov, are the prototypes of chaotic evolutions in classical dynamical systems. Here we provide a concise updated account of their quantum counterparts originally formulated by Emch, Narnhofer, Thirring…
Our context is Filippov systems defined on two-dimensional manifolds having a finite number of tangency points. We prove that topological transitivity is a necessary and sufficient condition for the occurrence of non-deterministic chaos…
Consider the ensemble of Gaussian random potentials $\{V^L(q)\}_{L=1}^\infty$ on the $d$-dimensional torus where, essentially, $V^L(q)$ is a real-valued trigonometric polynomial of degree $L$ whose coefficients are independent standard…
The dynamics of a nonequilibrium system can become complex because the system has many components (e.g., a human brain), because the system is strongly driven from equilibrium (e.g., large Reynolds-number flows), or because the system…
We continue the study of non-invertible topological dynamical systems with expanding behavior. We introduce the class of {\em finite type} systems which are characterized by the condition that, up to rescaling and uniformly bounded…
We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy.…
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…
This paper deals with the controllability of linear one-dimensional hyperbolic systems. Reformulating the problem in terms of linear difference equations and making use of infinite-dimensional realization theory, we obtain both necessary…
In the last decade it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the…
In this paper, we study diagonal hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and non-decreasing initial data. We remark that these…
Here, we introduce a novel method for obtaining chaotic dynamics based on the Montgomery conjecture for the pair correlation of zeros of the Riemann zeta function. Motivated by the conjecture, we present a recursive relation that reveals…
It is shown that the existence of the cosmic kinematic fast dynamos in Bianchi type IX rotating cosmological models, faces severe difficulties, due to the fact that in these models rotation increases without bounds, which is strictly…
We address the problem of applying the Kolmogorov-Sinai method of entropic analysis, expressed in a generalized non-extensive form, to the dynamics of the logistic map at the chaotic threshold, which is known to be characterized by a power…
Two-dimensional driven dissipative flows are generally integrable via a conservation law that is singular at equilibria. Nonintegrable dynamical systems are confined to n*3 dimensions. Even driven-dissipative deterministic dynamical systems…
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. As a result, the numerically…
By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction…
Through asymptotic expansion, the large-time behavior of incompressible Navier--Stokes flow in $n$-dimensional whole space is depicted. Especially, from their parabolic scalings, large-time behaviors of any terms on the expansion are…
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…