Related papers: Dynamical systems in cosmology
In this book are studied, from the perspective of the dynamical systems, several Universe models. In chapter 1 we give a bird's eye view on cosmology and cosmological problems. Chapter 2 is devoted to a brief review on some results and…
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…
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…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
Dark energy is one of the deepest puzzles in modern cosmology, and mounting evidence suggests that it is not just a cosmological constant but a genuinely dynamical component. Although cosmology and dynamical systems theory emerged from…
Cosmology is becoming an important tool to test particle physics models. We provide an overview of the standard model of cosmology with an emphasis on the observations relevant for testing fundamental physics.
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades…
We discuss the dynamical system approach applied to Higher Order Theories of Gravity. We show that once the theory of gravity has been specified, the cosmological equations can be written as a first-order autonomous system and we give…
To our best knowledge, there are no problem books on cosmology yet, that would include its spectacular recent achievements. We believe there is a strong need for such now, when cosmology is swiftly becoming a strict and vast science, and…
We note that in general there exist two basic aspects in any branch of physics, including cosmology - one dealing with the attributes of basic constituents and forces of nature, the other dealing with how structures arise from them and how…
This text consists on a series of introductory lectures on cosmology for mathematicians and physicists who are not specialized on the subject.
Methods and techniques of the theory of nonlinear dynamical systems and patterns can be useful in astrophysical applications. Some works on the subjects of dynamical astronomy, stellar pulsation and variability, as well as spatial…
Dynamical systems techniques are a powerful tool to analyse systems of ordinary differential equations, written in an appropriate form. For a given theory of gravity, the cosmological field equations typically lead to a system of ordinary…
Complex systems throughout Nature display structures and functions that are built and maintained, at least in part, by optimal energies flowing through them--not specific, ideal values, rather ranges in energy rate density below which…
A number of dynamical system formulations have been proposed over the last few years to analyse cosmological solutions in $f(R)$ gravity. The aim of this article is to provide a brief introduction to the different approaches, presenting…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
It is useful to study the space of all cosmological models from a dynamical systems perspective, that is, by formulating the Einstein field equations as a dynamical system using appropriately normalized variables. We will discuss various…
This review is an up-to-date account of the use of numerical relativity to study dynamical, strong-gravity environments in a cosmological context. First, we provide a gentle introduction into the use of numerical relativity in solving…
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…
A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…