相关论文: Chaos and frequent hypercyclicity for composition …

A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular-chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence…

Operator scrambling is a crucial ingredient of quantum chaos. Specifically, in the quantum chaotic system, a simple operator can become increasingly complicated under unitary time evolution. This can be diagnosed by various measures such as…

Chaos is a fundamental phenomenon in nonlinear dynamics, manifesting as irregular and unpredictable behavior across various physical systems. Among the diverse routes to chaos, intermittent chaos is a distinct transition pathway,…

The ergodic hypothesis outgrew from the ancient conception of motion as periodic or quasi periodic. It did cause a revision of our views of motion, particularly through Boltzmann and Poincar\'e: we discuss how Boltmann's conception of…

Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…

Guided by a geometric understanding developed in earlier works of Wang and Young, we carry out some numerical studies of shear-induced chaos. The settings considered include periodic kicking of limit cycles, random kicks at Poisson times,…

We present a generalization of bilateral weighted shift operators for the noncommutative multivariable setting. We discover a notion of periodicity for these shifts, which has an appealing diagramatic interpretation in terms of an infinite…

The harmonic oscillator is the paragon of physical models; conceptually and computationally simple, yet rich enough to teach us about physics on scales that span classical mechanics to quantum field theory. This multifaceted nature extends…

In this article we introduce a new class of Rolewicz-type operators in l_p, $1 \le p < \infty$. We exhibit a collection F of cardinality continuum of operators of this type which are chaotic and remain so under almost all finite linear…

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…

We give several equivalent characterization of aperiodicity of an element on locally compact group $G$, and give an intuition for "How strong does the aperiodicity of an element affect the existence of hypercyclic weighted translation…

In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself…

The question of whether a hypercyclic operator $T$ acting on a Fr{\'e}chet algebra $X$ admits or not an algebra of hypercyclic vectors (but 0) has been addressed in the recent literature. In this paper we give new criteria and…

Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…

What dynamical quantity is actually controlled by higher-order interactions in chaotic oscillator networks remains unclear. In amplitude-active systems, chaos is often interpreted through coherence, yet coherence is not the quantity that…

We extend a result of B\`{e}s, Martin, Peris and Shkarin by stating: $B_w$ is $\mathscr{F}$-weighted backward shift if and only if $(B_w,\dots, B_w^r)$ is $d$-$\mathscr{F}$, for any $r\in \mathbb{N}$, where $\mathscr{F}$ runs along some…

We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to…

Let $I$ be a countably infinite index set, and let $X$ be a Banach sequence space over $I.$ In this article, we characterize disjoint hypercyclic and supercyclic weighted pseudo-shift operators on $X$ in terms of the weights, the OP-basis,…

We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…

The presence of a period-doubling cascade in dynamical systems that depend on a parameter is one of the basic routes to chaos. It is rarely mentioned that there are virtually always infinitely many cascades whenever there is one. We report…