相关论文: Li-Yorke chaos for ultragraph shift spaces

We study the chaos of travelling waves (TW) in unidirectional chains of bistable maps. Previous numerical results suggested that this property is selective, {\sl viz.}\ given the parameters, there is at most a single (non-trivial) velocity…

In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behaviour of cellular automata, that the computational basis…

Recurrence determinism, one of the fundamental characteristics of recurrence quantification analysis, measures predictability of a trajectory of a dynamical system. It is tightly connected with the conditional probability that, given a…

A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal…

A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…

In this paper, we introduce a unified framework for defining Lin-Lu-Yau (LLY) Ricci curvature on both undirected and directed hypergraphs. By establishing upper bounds and monotonicity properties for the parameterized curvature…

We define new isomorphism-invariants for ergodic measure-preserving systems on standard probability spaces, called measure-theoretic chaos and measure-theoretic$^+$ chaos. These notions are analogs of the topological chaoses {\rm DC2} and…

This book chapter introduces to the concept of weak chaos, aspects of its ergodic theory description, and properties of the anomalous dynamics associated with it. In the first half of the chapter we study simple one-dimensional…

In this survey we describe a recently-developed technique for bounding the number (and controlling the typical structure) of finite objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by…

Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…

We define an ultragraph, which is a generalization of a directed graph, and describe how to associate a C*-algebra to it. We show that the class of ultragraph algebras contains the C*-algebras of graphs as well as the Exel-Laca algebras. We…

There is a long tradition of studying chaotic trajectories in systems whose integrability is broken by means of an external perturbation. Here we explore a different route to chaos, in the dynamics of extended bodies, which arises due to…

A recent quasiclassical description of a tunneling universe model is shown to exhibit chaotic dynamics by an analysis of fractal dimensions in the plane of initial values. This result relies on non-adiabatic features of the quantum…

An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…

We present a study of the recently discovered spatially-extended chaotic state known as spiral-defect chaos, which occurs in low-Prandtl-number, large-aspect-ratio Rayleigh-Benard convection. We employ the modulus squared of the space-time…

The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…

We introduce a new paradigm of 2D (electromagnetic) ray-chaos, featuring both guided and scattered rays in a dielectric layer with exponentially tapered refraction index backed by an undulated conductive surface, and illustrate its relevant…

Classical chaos arises from the inherent non-linearity of dynamical systems. However, quantum maps are linear; therefore, the definition of chaos is not straightforward. To address this, we study a quantum system that exhibits chaotic…

We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…

Transition from quasiperiodicity with many frequencies (i.e., a high-dimensional torus) to chaos is studied by using $N$-dimensional globally coupled circle maps. First, the existence of $N$-dimensional tori with $N\geq 2$ is confirmed…