Related papers: Effects of non-denumerable fixed points in finite …
A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection…
Dynamical Systems theory generally deals with fixed point iterations of continuous functions. Computation by Turing machine although is a fixed point iteration but is not continuous. This specific category of fixed point iterations can only…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…
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…
An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
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…
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 consider systems of n particles that move with constant velocity between collisions. Their total momentum but not necessarily their kinetic energy is preserved at collisions. As there are no further constraints, these systems are…
We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
In this paper, we investigate some dynamical properties near a nonhyperbolic fixed point. Under some conditions on the higher nonlinear terms, we establish a stable manifold theorem and a degenerate Hartman theorem. Furthermore, the finite…
Non-deterministic chaos is a new dynamical paradigm where a non-deterministic system is influenced by random perturbations to produce the appearance of complexity. The non-determinism is envisioned to occur only at a single point in phase…
Traditionally, Probability theory was dealing with limit theorems where 'limit" means that time tends to infinity. Questions about finite time dynamics (evolution) were always considered as, although important for practical applications,…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…
We show that a continuous map or a continuous flow on $\R^{n}$ with a certain recurrence relation must have a fixed point. Specifically, if there is a compact set W with the property that the forward orbit of every point in $\R^{n}$…
In this work, we study the dynamical systems analysis of phantom dark energy models considering a general potential. The stability analysis of the system shows that there is only one fixed point which could be the beginning of the universe…
Consider a three-dimensional vector field $F$ which generates a finite number of fixed points - what can we say on its unbounded dynamics? In this paper we tackle this question, and prove sufficient conditions for $F$ to have fixed points…
We argue that simple dynamical systems are factors of finite automata, regarded as dynamical systems on discontinuum. We show that any homeomorphism of the real interval is of this class. An orientation preserving homeomorphism of the…