Related papers: Some Variations of Transitivity for CR-dynamical s…
We study various ergodic properties of C*-dynamical systems inspired by unique ergodicity. In particular we work in a framework allowing for ergodic properties defined relative to various subspaces, and in terms of weighted means. Our main…
Deterministic dynamical systems such as the baker maps are useful to shed light on some of the conditions verified by deterministic models in non-equilibrium statistical physics. We investigate a 2D dynamical system, enjoying a weak form of…
Let (X,T) be a topologically transitive dynamical system. We show that if there is a subsystem (Y,T) of (X,T) such that (X\times Y, T\times T) is transitive, then (X,T) is strongly chaotic in the sense of Li and Yorke. We then show that…
Relations always play an important role in the study of topological dynamics. Proximal, distal and almost periodic relations are well studied in literature. We further this direction and analogously study the strongly proximal and weakly…
Many mechanical systems exhibit changes in their kinematic topology altering the mobility. Ideal contact is the best known cause, but also stiction and controlled locking of parts of a mechanism lead to topology changes. The latter is…
Let $K$ be an algebraically closed field of arbitrary characteristic, $X$ an irreducible variety and $Y$ an irreducible projective variety over $K$, both are not necessarily smooth. Let $f:X\rightarrow X$ and $g:Y\rightarrow Y$ be dominant…
Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…
We describe various strengthenings of the concept of topological transitivity. Especially when one departs from the family of invertible systems, a number of interesting properties arise. We present the architecture of implications among…
A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…
The "theory of open sub-functorial dynamics" is a new theory that defines interacting generalized dynamical systems. The interactions between these dynamics produce new dynamics which, of course, can then enter into other interactions. A…
Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…
In this paper we provide examples of topological dynamical systems having either finite or countable scrambled sets. In particular we study conditions for the existence of Li-Yorke, asymptotic and distal pairs in constant--length…
In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and…
Visual relationship reasoning is a crucial yet challenging task for understanding rich interactions across visual concepts. For example, a relationship 'man, open, door' involves a complex relation 'open' between concrete entities 'man,…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
In this work, we present several new findings regarding the concepts of orbit-transitivity, strict orbit-transitivity, $\omega$-transitivity, and $\mu$-open-set transitivity for self-maps on generalized topological spaces. Let $(X,\mu)$…
In this article, we examine the dynamical system of the $f(R,\mathcal{G})$ gravity model. This $f(R,G)$ model framework is composed of interactions between dark matter and scalar field through the linear coupling term. The key objective of…
The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time…
A dynamical system is a pair $(X,G)$, where $X$ is a compact metrizable space and $G$ is a countable group acting by homeomorphisms of $X$. An endomorphism of $(X,G)$ is a continuous selfmap of $X$ which commutes with the action of $G$. One…
One of the main features of adaptive systems is an oscillatory convergence that exacerbates with the speed of adaptation. Recently it has been shown that Closed-loop Reference Models (CRMs) can result in improved transient performance over…