Related papers: Cosmic infinity: A dynamical system approach
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
In this paper, we study in detail a perfect fluid cosmological model with time-varying "constants" using dimensional analysis and the symmetry method. We examine the case of variable "constants" in detail without considering the perfect…
We consider a cosmology in which the final stage of the Universe is neither accelerating nor decelerating, but approaches an asymptotic state where the scale factor becomes a constant value. In order to achieve this, we first bring in a…
In this paper we discuss a cosmological model for a universe with self-regulating features. We set up the theoretical framework for the model and determine the time evolution of the scale-factor $a(t)$. It is shown that such a universe…
We use the phase plane analysis technique of Madsen and Ellis to consider a universe with a true cosmological constant as well as a cosmological "constant" that is decaying. Time symmetric dynamics for the inflationary era allows eternally…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
Dynamical system methods are used in the study of the stability of spatially flat homogeneous cosmologies within a large class of generalized modified gravity models in the presence of a relativistic matter-radiation fluid. The present…
Black holes are usually studied without including effects of the expanding universe. However in some recent studies black holes have been embedded in an expanding universe, in order to determine the interplay, if any, of these two dynamical…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
Non-reciprocal interactions are a generic feature of non-equilibrium systems. We define a non-reciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for…
Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…
We discuss recent developments related to certain blow up methods suitable for the analysis of cosmological singularities and asymptotics. We review results obtained in a variety of currently popular themes and describe ongoing research…
A new approach for arbitrary dimension to the Friedmann cosmological models is presented. Taking suitable changes of the parameters of the spacetime the harmonic motion equations appear, where the curvature determines the angular frequency.…
Some cosmological models based on the gravitational theory $f(R) = R+\zeta R^2$, and on fluids obeying to the equations of state of Redlich-Kwong, Berthelot, and Dieterici are proposed for describing smooth transitions between different…
We perform a detailed phase-space analysis of a class of k-essence cosmology. We find the critical points can be divided into three classes: points unstable but the model stable, both points and the model stable, points stable but the model…
In this paper, we model the bounce phase, stability, and the reconstruction of the universe by non-minimal kinetic coupling. In the process, we obtained importance information about the energy density and the matter pressure of the universe…
In cosmology, the cosmic curvature $K$ and the cosmological constant $\Lambda$ are two important parameters, and the values have strong influence on the behavior of the universe. In the context of normal cosmology, under the ordinary…
In this paper we analyze the asymptotic behavior of Cardassian cosmological models filled with a perfect fluid and a scalar field with an exponential potential. Cardassian cosmologies arise from modifications of the Friedmann equation, and…
Future singularities arising in a family of models for the expanding Universe, characterized by sharing a convenient parametrization of the energy budget in terms of the deceleration parameter, are classified. Finite-time future…
The big bounce singularity of a simple 5D cosmological model is studied. Contrary to the standard big bang space-time singularity, this big bounce singularity is found to be an event horizon at which the scale factor and the mass density of…