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Dynamical Systems And Cosmology

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Dynamical Systems And Cosmology

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Author : A.A. Coley
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-31

Dynamical Systems And Cosmology written by A.A. Coley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-31 with Science categories.

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 differential equations. In this book we discuss cosmological models as dynamical systems, with particular emphasis on applications in the early Universe. We point out the important role of self-similar models. We review the asymptotic properties of spatially homogeneous perfect fluid models in general relativity. We then discuss results concerning scalar field models with an exponential potential (both with and without barotropic matter). Finally, we discuss the dynamical properties of cosmological models derived from the string effective action. This book is a valuable source for all graduate students and professional astronomers who are interested in modern developments in cosmology.

Dynamical Systems And Cosmology

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Author : A.A. Coley
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Dynamical Systems In Cosmology

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Author : J. Wainwright
language : en
Publisher: Cambridge University Press
Release Date : 2005-06-30

Dynamical Systems In Cosmology written by J. Wainwright and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-30 with Science categories.

This authoritative volume shows how modern dynamical systems theory can help us in understanding the evolution of cosmological models. It also compares this approach with Hamiltonian methods and numerical studies. A major part of the book deals with the spatially homogeneous (Bianchi) models and their isotropic subclass, the Friedmann-Lemaitre models, but certain classes of inhomogeneous models (for example, 'silent universes') are also examined. The analysis leads to an understanding of how special (high symmetry) models determine the evolution of more general families of models; and how these families relate to real cosmological observations. This is the first book to relate modern dynamical systems theory to both cosmological models and cosmological observations. It provides an invaluable reference for graduate students and researchers in relativity, cosmology and dynamical systems theory.

Dynamical Systems In Cosmology

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Author : Nyein Chan
language : en
Publisher:
Release Date : 2012

Dynamical Systems In Cosmology written by Nyein Chan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.

Dynamical Systems In Cosmology And Astrophysics

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Author : Ulf Nilsson
language : en
Publisher:
Release Date : 1998

Dynamical Systems In Cosmology And Astrophysics written by Ulf Nilsson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Astrophysics categories.

Dynamical Systems In Cosmology

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Author : N. Chan
language : en
Publisher:
Release Date : 2012

Dynamical Systems In Cosmology written by N. Chan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.

In this PhD thesis, the role of dynamical systems in cosmology has been studied. Many systems and processes of cosmological interest can be modelled as dynamical systems. Motivated by the concept of hypothetical dark energy that is believed to be responsible for the recently discovered accelerated expansion of the universe, various dynamical dark energy models coupled to dark matter have been investigated using a dynamical systems approach. The models investigated include quintessence, three-form and phantom fields, interacting with dark matter in different forms. The properties of these models range from mathematically simple ones to those with better physical motivation and justification. It was often encountered that linear stability theory fails to reveal behaviour of the dynamical systems. As part of this PhD programme, other techniques such as application of the centre manifold theory, construction of Lyapunov functions were considered. Applications of these so-called methods of non-linear stability theory were applied to cosmological models. Aforementioned techniques are powerful tools that have direct applications not only in applied mathematics, theoretical physics and engineering, but also in finance, economics, theoretical immunology, neuroscience and many more. One of the main aims of this thesis is to bridge the gap between dynamical systems theory, an area of applied mathematics, and cosmology, an exciting area of physics that studies the universe as a whole.

Methods In The Qualitative Theory Of Dynamical Systems In Astrophysics And Gas Dynamics

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Author : O.I. Bogoyavlensky
language : en
Publisher: Springer
Release Date : 1985-08

Methods In The Qualitative Theory Of Dynamical Systems In Astrophysics And Gas Dynamics written by O.I. Bogoyavlensky and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-08 with Mathematics categories.

Homogeneous cosmological models, self-similar motion of self-gravitating gas and motion of gas with homogeneous deformation have important applica tions in the theory of evolution of the universe. In particular they can be applied to the theory of explosions of stars, formation of galaxies, pulsation of alternating stars etc. The equations of general relativity and Newtonian gas dynamics in the cases mentioned above are reduced to systems of a finite (but quite large) number of ordinary differential equations. In the last two decades these multi-dimensional dynamical systems were and still are being analyzed by means of traditional analytic and numerical methods. Important dynamical modes of some solutions were thus established. These include oscillatory modes of the space-time metric near a cosmological singularity, self-similar motion of self-gravitating gas with a shock wave and an expanding cavity inside (as in an explosion of a star), collapse of an ellipsoid of self-gravitating dust into a disc and others. However the multi dimensional dynamical systems in question are so complex, that a complete analysis of all dynamical modes of the solutions by means of well-known tra ditional analytic methods does not seem feasible. Therefore the development of effective methods of qualitative analysis of multi-dimensional dynamical systems and their application to the problems of astrophysics and gas dynamics previ ously unsolved by traditional methods becomes especially urgent.

Order And Chaos In Dynamical Astronomy

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Author : George Contopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-06-16

Order And Chaos In Dynamical Astronomy written by George Contopoulos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-16 with Science categories.

This book is one of the first to provide a general overview of order and chaos in dynamical astronomy. The progress of the theory of chaos has a profound impact on galactic dynamics. It has even invaded celestial mechanics, since chaos was found in the solar system which in the past was considered as a prototype of order. The book provides a unifying approach to these topics from an author who has spent more than 50 years of research in the field. The first part treats order and chaos in general. The other two parts deal with order and chaos in galaxies and with other applications in dynamical astronomy, ranging from celestial mechanics to general relativity and cosmology.

Impact Of Modern Dynamics In Astronomy

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Author : Jacques Henrard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Impact Of Modern Dynamics In Astronomy written by Jacques Henrard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

Modem dynamics is increasingly participating in the solution of problems raised by as tronomical observations. This new relationship is being fostered on one side by the im provements in the observations, which in recent years contributed several discoveries of new systems, such as the objects in the Kuiper belt, the pulsar and star companions, to speak only of the most striking ones, and, on the other hand, by the progresses in modem dynamics. The progresses in modem dynamics are due to two factors: the dissemination of fast computers, allowing the numerical studies of very complex systems by a large number of scientists, and the improvement in our understanding of the complex behaviour of Hamiltonian systems. KAM and Nekhorochev theories have shed a light on the subtle and surprizing interplays between regular and chaotic motions; numerical experiments and analytical approximations have shown how these peculiarities are indeed present in astronomically important systems and are instrumental in understanding their formation and evolution.

Modified Gravity And Cosmology

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Author : Emmanuel N. Saridakis
language : en
Publisher: Springer Nature
Release Date : 2021-12-10

Modified Gravity And Cosmology written by Emmanuel N. Saridakis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-10 with Science categories.

With a focus on modified gravity this book presents a review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. General Relativity and the ΛCDM framework are currently the standard lore and constitute the concordance paradigm of cosmology. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology in the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. In this review all extended theories and scenarios are first examined under the light of theoretical consistency, and are then applied in various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology has been able to offer in the last two decades. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature, allowing readers to get a clear overview of the state of the art and where the field of modified gravity is likely to go. This work was performed in the framework of the COST European Action “Cosmology and Astrophysics Network for Theoretical Advances and Training Actions” - CANTATA.

Dynamical Systems And Cosmology

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