Related papers: Cosmic infinity: A dynamical system approach
In this paper, we investigate the theoretical possibility that a Lagrangian fixed point, when applied to cosmological models, can drive dynamical evolution towards a bouncing universe. We analyze the physics of a Lagrangian fixed point…
The late time accelerated expansion of the universe can be realized using scalar fields with given self-interacting potentials. Here we consider a straightforward approach where a three cosmic fluid mixture is assumed. The fluids are…
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…
Centre manifold theory is applied to some dynamical systems arising from spatially homogeneous cosmological models. Detailed information is obtained concerning the late-time behaviour of solutions of the Einstein equations of Bianchi type…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
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 present a rich class of exact solutions which contains radiation-dominated and matter-dominated models for the early and late universe. They include a variable cosmological ``constant'' which is derived from a higher dimension and…
An accelerated universe should naturally have a vacuum energy density determined by its dynamical curvature. The cosmological constant is most likely a temporary description of a dynamical variable that has been drastically evolving from…
The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
Dark energy models can be seen as dynamical systems. In this paper we show that multi-field models with a curved field space give rise to new critical points and we analyse their stability. These are new accelerating solutions in late-time…
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 present two methods for describing, from a pedagogical point of view, the solutions of Einstein's equations applied to a homogeneous and isotropic universe. In the first method, we define an effective gravitational potential of the…
This thesis is concerned with global properties of those cosmological solutions of Einstein's field equations which obey accelerated expansion into the future driven by a non-vanishing cosmological constant, as suggested by current…
In this paper, we study the phase space of cosmological models in the context of Einstein-Gauss-Bonnet theory. More specifically, we consider a generalized dynamical system that encapsulates the main features of the theory and for the cases…
A new cosmological model based on the de Sitter gravity is investigated by dynamical analysis and numerical discussions. Via some transformations, the evolution equations of this model can form an autonomous system with 8 physical critical…
Universe structure emerges in the unreduced, complex-dynamical interaction process with the simplest initial configuration (two attracting homogeneous fields). The unreduced interaction analysis avoiding any perturbative model gives…
The theory of the dynamical systems is a very complex subject which has brought several surprises in the recent past in connection with the theory of chaos and fractals. The application of the tools of the dynamical systems in cosmological…
We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle…
We present a detailed investigation of the cosmological dynamics based on $\exp (-R/{\Lambda})$ gravity. We apply the dynamical system approach to both the vacuum and matter cases and obtain exact solutions and their stability in the finite…