相关论文: Li-Yorke and Devaney chaotic uniform dynamical sys…
In this work we study possibility of chaos formation in the dynamics governed by paradigmatic model of Cavity Quantum Electrodynamics, the so called James-Cammings model. In particular we consider generalized JC model. It is shown that even…
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,…
We show that for a non-trivial transitive dynamical system, it has a dense Mycielski invariant strongly scrambled set if and only if it has a fixed point, and it has a dense Mycielski invariant $\delta$-scrambled set for some $\delta>0$ if…
We investigate in detail a new class (GOOFy) of transformations for bosonic and fermionic fields that leave the Lagrangian density unchanged. The transformations act upon complex scalar fields \Phi and \Phi^\dagger employing generalized…
In the present paper, an essential generalization of the symbolic dynamics is considered. We apply the notions of abstract self-similar sets and the similarity map for a chaos introduction, which orbits are expanded among infinitely many…
In this paper we study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self maps on a compact space $X$. We derive necessary and sufficient conditions for the system to exhibit complex dynamical…
The aim of the paper is to correct and improve some results concerning distributional chaos of type 3. We show that in a general compact metric space, distributional chaos of type 3, denoted DC3, even when assuming the existence of an…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
We define and study stronger forms of Devaney chaos and name it as $\mathscr{F}-$Devaney chaos, where $\mathscr{F}$ is a family of subsets of $\mathbb{N}$. Examples of maps which is $\mathscr{F}_t-$Devaney chaotic but not…
We introduce uniformly vertex-transitive graphs as vertex-transitive graphs satisfying a stronger condition on their automorphism groups, motivated by a problem which arises from a Sinkhorn-type algorithm. We use the derangement graph…
In order to understand the parameters of the standard model of electroweak and strong interactions, one needs to embed the standard model into some larger theory that accounts for the observed values. This means some additional sector is…
The Denjoy-Wolff theorem is a foundational result in complex dynamics, which describes the dynamical behaviour of the sequence of iterates of a holomorphic self-map $f$ of the unit disc $\mathbb{D}$. Far less well understood are…
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…
In this paper, we discuss the relationship between Li-Yorke chaos and distributional chaos in a sequence. We point out the set of all distributional $\delta$-scramble pairs in the sequence $Q$ is a $G_\delta$ set, and prove that Li-Yorke…
We derive a conditional variational principle of the saturated set for systems with the non-uniform structure. Our result applies to a broad class of systems including beta-shifts, S-gap shifts and their factors.
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…
In this work the stability of perturbed linear time-varying systems is studied. The main features of the problem are threefold. Firstly, the time-varying dynamics is not required to be continuous but allowed to have jumps. Also the system…
In their celebrated "Period three implies chaos" paper, Li and Yorke proved that if a continuous interval map f has a period 3 point then there is an uncountable scrambled set S on which f has very complicated dynamics. One question arises…
We give an equivalent definition of Devaney chaotic semiflow in terms of eventual sensitivity, the notion recently introduced by C.~Good, R.~Leek, and J.~Mitchell. As a consequence, we prove a version of Auslander-Yorke dichotomy for the…
In the following text for vector space $V$ over field $F$ we compute all eigenvalues of weighted generalized shift $\sigma_{\varphi,\mathfrak{w}}:V^\Gamma\to V^\Gamma$ (and generalized shift $\sigma_\varphi:V^\Gamma\to V^\Gamma$) for…