Related papers: Chaos for foliated spaces and pseudogroups
Weak chaos in high-dimensional conservative systems can be characterized through sticky effect induced by invariant structures on chaotic trajectories. Suitable quantities for this characterization are the higher cummulants of the finite…
We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.
This paper investigates the correlation between $k$-type dynamical properties of $\mathbb{Z}^d$-actions on compact metric spaces and their induced actions on the corresponding hyperspaces. We extend the classical results from discrete…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…
We generalize the Cauchy-Davenport theorem to locally compact groups.
We provide evidence of an extreme form of sensitivity to initial conditions in a family of one-dimensional self-ruling dynamical systems. We prove that some hyperchaotic sequences are closed-form expressions of the orbits of these…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
For a general discrete dynamics on a Banach and Hilbert spaces we give necessary and sufficient conditions of the existence of bounded solutions under assumption that the homogeneous difference equation admits an discrete dichotomy on the…
The topological Molino's description of equicontinuous foliated spaces, studied by the first author and Moreira Galicia, gives conditions to reduce their study to the particular case where the holonomy pseudogroup can be represented by a…
It is revealed that a special kind of Poisson stable point, which we call an unpredictable point, gives rise to the existence of chaos in the quasi-minimal set. The existing definitions of chaos are formulated in sets of motions. This is…
We consider here a recently proposed geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor…
We show, using covariant Lyapunov vectors in addition to standard Lyapunov analysis, that there exists a set of collective Lyapunov modes in large chaotic systems exhibiting collective dynamics. Associated with delocalized Lyapunov vectors,…
A system of interacting particles described by stochastic differential equations is considered. As oppopsed to the usual model, where the noise perturbations acting on different particles are independent, here the particles are subject to…
The asymptotic distance between trajectories $d_{\infty}$, is studied in detail to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponents, and it allows for a…
Based on a coupling approach, we prove uniform in time propagation of chaos for weakly interacting mean-field particle systems with possibly non-convex confinement and interaction potentials. The approach is based on a combination of…
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…
Let (X,T) be a topologically transitive dynamical system. We show that if there is a subsystem (Y,T) of (X,T) such that (X\times Y, T\times T) is transitive, then (X,T) is strongly chaotic in the sense of Li and Yorke. We then show that…
In this paper, we introduce several new types and generalizations of the concepts distributional chaos and Li-Yorke chaos. We consider the general sequences of binary relations acting between metric spaces, while in a separate section we…
This article tackles a fundamental long-standing problem in quantum chaos, namely, whether quantum chaotic systems can exhibit sensitivity to initial conditions, in a form that directly generalizes the notion of classical chaos in phase…
In this paper, we give characterizations of distributional chaos and mean Li$-$Yorke chaos for weighted backward shifts acting on general Fr\'echet sequence spaces. As an application, we derive criteria for these two types of chaos in the…