Related papers: Dynamical Systems in Cosmology
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…
We use molecular dynamics simulations to compute the Lyapunov spectra of many-particle systems resembling simple fluids in thermal equilibrium and in non-equilibrium stationary states. Here we review some of the most interesting results and…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
We review the role of fluids in cosmology by first introducing them in General Relativity and then by applying them to a FRW Universe's model. We describe how relativistic and non-relativistic components evolve in the background dynamics.…
The present work is an example of the application of the dynamical system analysis in the context of cosmology. Here cosmic evolution is considered in the background of homogeneous and isotropic flat Friedmann-Lema\^{i}tre-Robertson-Walker…
Recent work in dynamical systems theory has shown that many properties that are associated with irreversible processes in fluids can be understood in terms of the dynamical properties of reversible, Hamiltonian systems. That is,…
We introduce the notion of the cosmic numbers of a cosmological model, and discuss how they can be used to naturally classify models according to their ability to solve some of the problems of the standard cosmological model.
Effective equations often provide powerful tools to develop a systematic understanding of detailed properties of a quantum system. This is especially helpful in quantum cosmology where several conceptual and technical difficulties…
The evolution of a class of inhomogeneous spherically symmetric universe models possessing a varying cosmological term and a material fluid, with an adiabatic index either constant or not, is studied.
We examine spinfoam cosmology by use of a simple graph adapted to homogeneous cosmological models. We calculate dynamics in the isotropic limit, and provide the framework for the aniostropic case. The dynamical behaviour is calculating…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
In the present work we investigate the stability of the k-essence models allowing upto quadratic terms of the kinetic energy. The system of field equations is written as an autonomous system in terms of dimensionless variables and the…
We study the cosmological stability of a class of theories with a dynamical preferred frame. For a range of actions, we find cosmological solutions which are compatible with observations of the recent history of the Universe: a matter…
In this thesis, we used dynamical systems analysis to find the qualitative behaviour of some dark energy models. Specifically, dynamical systems analysis of quintessence scalar field models, chameleon scalar field models and holographic…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
For several independent reasons, the idea that notorious sources of entropy could exist in the Universe has been recently revived. Taking advantage of a new framework accounting for non-equilibrium processes in cosmology, we explicitly…
Spatially homogeneous field theories are studied in the framework of dynamical system theory. In particular we consider a model of inflationary cosmology and a Yang-Mills-Higgs system. We discuss also the role of quantum chaos and its…
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…