Related papers: Multishadowing in topological dynamics
Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
Many biological and man-made networked systems are characterized by the simultaneous presence of different sub-networks organized in separate layers, with links and nodes of qualitatively different types. While during the past few years…
We introduce topological definitions of expansivity, shadowing, and chain recurrence for homeomorphisms. They generalize the usual definitions for metric spaces. We prove various theorems about topologically Anosov homeomorphisms (maps that…
Let $(X,G,\Phi)$ be a dynamical system, where $X$ is compact Hausdorff space, and $G$ is a countable discrete group. We investigate shadowing property and mixing between subshifts and general dynamical systems. For the shadowing property,…
This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…
The concept of node walk in graphs and complex networks has been addressed, consisting of one or more nodes that move into adjacent nodes, henceforth incorporating the respective connections. This type of dynamics is then applied to subsume…
A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…
To link the Auslander point dynamics property with topological transitivity, in this paper we introduce dynamically compact systems as a new concept of a chaotic dynamical system $(X,T)$ given by a compact metric space $X$ and a continuous…
Establishing the existence of periodic orbits is one of the crucial and most intricate topics in the study of dynamical systems, and over the years, many methods have been developed to this end. On the other hand, finding closed orbits in…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…
In this paper, subsystems with shadowing property for $\mathbb{Z}^{k}$-actions are investigated. Let $\alpha$ be a continuous $\mathbb{Z}^{k}$-action on a compact metric space $X$. We introduce the notions of pseudo orbit and shadowing…
In this article, we investigate the relationship between the shadowing property of set-valued maps and their associated inverse limit systems. We show that if a set-valued map is expansive and open in the context of set-valued dynamics,…
In this paper we study local stable/unstable sets of sensitive homeomorphisms with the shadowing property defined on compact metric spaces. We prove that local stable/unstable sets always contain a compact and perfect subset of the space.…
We investigate the dynamics of substitution subshifts and their associated tiling spaces. For a given subshift, the associated tiling spaces are all homeomorphic, but their dynamical properties may differ. We give criteria for such a tiling…
In this paper, some characterizations about transitivity, mildly mixing property, $\mathbf{a}$-transitivity, equicontinuity, uniform rigidity and proximality of Zadeh's extensions restricted on some invariant closed subsets of the space of…
We examine certain phenomena in $C^1$-dynamics from a viewpoint of shadowing and improve a known result on hyperbolic sets. We also review a result on the stability of attractor boundaries from the same viewpoint and derive several…
We find sufficient conditions for commutative non-autonomous systems on certain metric spaces to be topologically stable. In particular, we prove that (i) Every mean equicontinuous, mean expansive system with strong average shadowing…
The article presents a new perspective on the isomorphism problem for non-ergodic measure-preserving dynamical systems with discrete spectrum which is based on the connection between ergodic theory and topological dynamics constituted by…