Related papers: Limitations of the asymptotic approach to dynamics
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse…
In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
We study the asymptotic behavior of random time changes of dynamical systems. As random time changes we propose three classes which exhibits different patterns of asymptotic decays. The subordination principle may be applied to study the…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
We study the asymptotic behavior, as time t goes to infinity, of nonautonomous dynamical systems involving multiscale features. These systems model the emergence of various collective behaviors in game theory, as well as the asymptotic…
We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…
Let $(X,f_{1,\infty})$ be a nonautonomous dynamical system. In this paper we summarize known definitions of periodic points for general nonautonomous dynamical systems and propose a new, very natural, definition of asymptotic periodicity.…
In this paper, we introduce the concept of random time changes in dynamical systems. The sub- ordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
In the paper we define and characterize the asynchronous systems from the point of view of their autonomy, determinism, order, non-anticipation, time invariance, symmetry, stability and other important properties. The study is inspired by…
This paper is a survey of extensions to finite automata theory to model real-time systems as well as systems exhibiting mixed discrete-continuous behavior. Real-time systems maintain a continuous and timely interaction with the environment,…
To characterize local finite-time properties associated with transient chaos in open dynamical systems, we introduce an escape rate and fractal dimensions suitable for this purpose in a coarse-grained description. We numerically illustrate…
The collective dynamics of interacting dynamical units on a network crucially depends on the properties of the network structure. Rather than considering large but finite graphs to capture the network, one often resorts to graph limits and…
The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium of the…
The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…
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…
In this Article, several aspects of the asymptotic dynamics of finite-dimensional open quantum systems are explored. First, after recalling a structure theorem for the peripheral map, we discuss sufficient conditions and a characterization…
Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly…
A notion of time is fundamental in the study of dynamical systems. Time arises as a standalone dynamical system and also in solutions or trajectories as a special kind of map between systems. We characterize time by a universal property and…