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We propose as a generalization of an idea of Ruelle to describe turbulent fluid flow a chaotic hypothesis for reversible dissipative many particle systems in nonequilibrium stationary states in general. This implies an extension of the…
We show that an embedding of a fixed 0-dimensional compact space $K$ into the \v{C}ech--Stone remainder $\omega^*$ as a nowhere dense P-set is the unique generic limit, a special object in the category consisting of all continuous maps from…
This paper is a sequel to Chaika and Krishnan [arXiv:1612.00434]. We again consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice Z^d. We assume that once walks meet, they…
We present a method to detect the unstable periodic orbits of a multidimensional chaotic dynamical system. Our approach allows us to locate in an efficient way the unstable cycles of, in principle, arbitrary length with a high accuracy.…
Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…
Chaotic systems exhibit rich quantum dynamical behaviors ranging from dynamical localization to normal diffusion to ballistic motion. Dynamical localization and normal diffusion simulate electron motion in an impure crystal with a vanishing…
We propose a method which can effectively stabilize fixed points in the classical and quantum dynamics of a phase-sensitive chaotic system with feedback. It is based on feeding back a selected quantum sub-ensemble whose phase and amplitude…
We revisit the global dynamics of unified dark matter cosmological models and analyze it in a new dynamical system setting. In particular, by defining a suitable set of variables we obtain a bounded variable space, a feature that allows a…
We consider the problem of finding embeddings of arc-like continua in the plane for which each point in a given subset is accessible. We establish that, under certain conditions on an inverse system of arcs, there exists a plane embedding…
We present the first report on inverse chaos synchronization between bi-directionally non-linearly and linearly coupled variable multiple time delay Ikeda systems. The results are of certain importance in secure chaos-based communication…
We show the existence of a dynamical system without any distributionally scrambled pair which is semiconjugated to a distributionally chaotic factor.
Random magnetic field configurations are ubiquitous in nature. Such fields lead to a variety of dynamical phenomena, including localization and glassy physics in some condensed matter systems and novel transport processes in astrophysical…
We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
In this article, we show that a chaotic behavior can be found on a cube with arbitrary finite dimension. That is, the cube is a quasi-minimal set with Poincare chaos. Moreover, the dynamics is shown to be Devaney and Li-Yorke chaotic. It…
In this paper we solve two open problems concerning distributional chaos in non-autonomous discrete dynamical systems stated in [4] and [17]. In the first problem it is wondered if the limit function of pointwise convergent non-autonomous…
This paper studies distributional chaos in non-autonomous discrete systems generated by given sequences of maps in metric spaces. In the case that the metric space is compact, it is shown that a system is Li-Yorke{\delta}-chaotic if and…
We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet that is periodically kicked with a delta function…
We investigate the transport of energy, magnetization, etc. in several finite one-dimensional (1D) quantum systems only by solving the corresponding time-dependent Schroedinger equation. We explicitly renounce on any other…
A "dispersive quantum system" is a quantum system which is both isolated and non-time reversal invariant. This article presents precise definitions for those concepts and also a characterization of dispersive quantum systems within the…