Related papers: Some Variations of Transitivity for CR-dynamical s…
Many real-world complex systems including human interactions can be represented by temporal (or evolving) networks, where links activate or deactivate over time. Characterizing temporal networks is crucial to compare such systems and to…
Connecting curves have been shown to organize the rotational structure of strange attractors in three-dimensional dynamical systems. We extend the description of connecting curves and their properties to higher dimensions within the special…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…
In this note we consider dynamical systems $(X,G)$ on a Cantor set $X$ satisfying some mild technical conditions. The considered class includes, in particular, minimal and transitive aperiodic systems. We prove that two such systems…
Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…
Theoretical challenges in understanding the nature of glass and the glass transition remain significant open questions in statistical and condensed matter physics. As a prototypical example of complex physical systems, glasses and the…
Stability and bifurcation properties of one-dimensional discrete dynamical systems with positivity, which are derived from continuous ones by tropical discretization, are studied. The discretized time interval is introduced as a bifurcation…
In this work we study the main dynamical properties of the push-forward map, a transformation in the space of probabilities P(X) induced by a map T: X \to X, X a compact metric space. We also establish a connection between topological…
Dynamical systems are a broad class of mathematical tools used to describe the evolution of physical and computational processes. Traditionally these processes model changing entities in a static world. Picture a ball rolling on an empty…
This article is devoted to a description of the dynamics of the phase flow of monotone contact Hamiltonian systems. Particular attention is paid to locating the maximal attractor (or repeller), which could be seen as the union of compact…
We discuss the dynamics of finite systems within molecular dynamics models. Signatures of a critical behavior are analyzed and compared to experimental data both in nucleus-nucleus and metallic cluster collisions. We suggest the possibility…
One main task of smooth dynamical systems consists in finding a good decomposition into elementary pieces of the dynamics. This paper contributes to the study of chain-recurrence classes. It is known that $C^1$-generically, each…
Let $(X, f)$ be a topological dynamical system and $\mathcal {F}$ be a Furstenberg family (a collection of subsets of $\mathbb{N}$ with hereditary upward property). A point $x\in X$ is called an $\mathcal {F}$-transitive point if for every…
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…
A modified theory of general relativity is proposed, where the gravitational constant is replaced by a dynamical variable in space-time. The dynamics of the gravitational coupling is described by a family of parametrized null geodesics,…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
This paper studies the behavior of dynamical systems in non-compact spaces, specifically focusing on the concepts of global attractors and shadowing. Let $K$ be a compact global attractor. We show that the shadowing property holds in…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
Modified gravity is one of the most favorable candidates for explaining the current accelerating expansion of the Universe. In this regard, we study the viability of an alternative gravitational theory, namely $f(R,G)$, by imposing energy…