相关论文: Distributional Chaos and Dendrites
Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of…
For any continuous self-map of a compact metric space, we prove a saturation of distributionally scrambled Mycielski sets under a type of shadowing and the chain transitivity.
We explore connections among the regional proximal relation, the asymptotic relation and the distal relation for a topological dynamical system with the shadowing property, and show that if a Devaney chaotic system has the shadowing…
In this chapter, we discuss avalanches in glasses and disordered systems, and the macroscopic dynamical behavior that they mediate. We briefly review three classes of systems where avalanches are observed: depinning transition of disordered…
In this article, we provide a sufficient condition which gives Devaney chaos and distributional chaos for Cowen-Douglas operators. In fact, we obtain a distributionally chaotic criterion for bounded linear operators on Banach spaces.
The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled…
We consider stable periodic helixes as a generalization of stable periodic orbits. We see that in the studied class of iterated functions Chaos always arise suddenly. Therefore, we shall study the route from chaos to order rather than the…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing…
Collective chaos is shown to emerge, via a period-doubling cascade, from quasiperiodic partial synchronization in a population of identical inhibitory neurons with delayed global coupling. This system is thoroughly investigated by means of…
A compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar features of tunneling in certain…
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…
In this paper, we investigate the distributional chaos of the composition operator $T_{\varphi}:f\mapsto f\circ\varphi$ on $L^{p}(X,\mathcal{B},\mu)$, $1\leq p <\infty$. We provide a characterization and practical sufficient conditions on…
Passive scalar mixing, produced by Lagrangian chaos generated a) by quasi-periodic (integrable) motion of three quasi-point vortices and b) by chaotic motion of three and six quasi-point vortices, has been studied and compared with…
While a generic open quantum system decays to its steady state, continuous time crystals (CTCs) develop spontaneous oscillation and never converge to a stationary state. Just as crystals develop correlations in space, CTCs do so in time.…
A model of nonlinear resonance as a periodically perturbed pendulum is considered, and a new method of analytical estimating the width of a chaotic layer near the separatrices of the resonance is derived for the case of slow perturbation…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic…
The transition from hard/soft turbulence to deterministic chaos in freely decaying fluid dynamics (incompressible and compressible) has been studied using the results of laboratory measurements and numerical simulations. The notion of…