Related papers: Preservation of shadowing in discrete dynamical sy…

Molecular dynamics refers to the computer simulation of a material at the atomic level. An open problem in numerical analysis is to explain the apparent reliability of molecular dynamics simulations. The difficulty is that individual…

We develop a new metric and inverse-limit framework for Deaconu-Renault systems arising from local homeomorphisms between open subsets of locally compact zero-dimensional spaces. Our starting point is the Paterson-type compactification of…

Predictability horizon properties of chaotic dynamical systems can be related to their spectral properties. It is shown, using this relationship, that the spectral properties of the leading large-scale climate daily indices indicate a…

Switches in real systems take many forms, such as impacts, electronic relays, mitosis, and the implementation of decisions or control strategies. To understand what is lost, and what can be retained, when we model a switch as an…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

We provide an alternative view of some results in [1, 3, 11]. In particular, we prove that (1) if a continuous self-map of a compact metric space has the shadowing, then the union of the basins of terminal chain components is a dense…

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…

We describe the dynamical formation of the shadow of a collapsing star in a Hayward spacetime in terms of an observer far away from the center and a free falling observer. By solving the time-like and light-like radial geodesics we…

We explore the characteristics of shadows for a general class of spherically symmetric, static spacetimes, which may arise in general relativity or in modified theories of gravity. The chosen line element involves a sum (with constant but…

We investigate a shadowing property which appears naturally in the study of piecewise monotonic maps of the interval. It turns out to be a weak form of the rank one property, a well-known notion in abstract ergodic theory. We show that this…

We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…

We show that shadowing is a generic property among continuous maps and surjections on a large class of locally connected one-dimensional continua.

This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A…

While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…

We define the concept of $(\mathscr{F},\mathscr{G})-$shadowing property on uniform space and say it as a topological $(\mathscr{F},\mathscr{G})-$shadowing property. We show that topological shadowing, topological…

We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…

We obtain the shadow cast induced by the rotating black hole with an anisotropic matter. A Killing tensor representing the hidden symmetry is derived explicitly. The existence of separability structure implies a complete integrability of…

Consider a singularly perturbed system $$\epsilon u_t=\epsilon^2 u_{xx} + f(u,x,\epsilon),\quad u\in {\Bbb R}^n,x\in{\Bbb R},t\geq 0. $$ Assume that the system has a sequence of regular and internal layers occurring alternatively along the…

For nonautonomous and nonlinear differential and difference equations depending on a parameter, we formulate sufficient conditions under which they exhibit $C^k$, $k\in \N$ shadowing with respect to a parameter. Our results are applicable…

We study the geometry and dynamics of both isolated and dynamical trapping horizons by considering the allowed variations of their foliating two-surfaces. This provides a common framework that may be used to consider both their possible…