Dynamical Systems and Cosmology

Dynamical Systems and Cosmology
Author: A.A. Coley
Pages: 195
ISBN: 9789401703277
Available:
Release: 2013-04-17
Editor: Springer Science & Business Media
Language: en

Explanation of the Book:

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 in Cosmology

Dynamical Systems in Cosmology
Author: J. Wainwright,G. F. R. Ellis
Pages: 343
ISBN: 9780521554572
Available:
Release: 1997-01-28
Editor: Cambridge University Press
Language: en

Explanation of the Book:

This is the first book to show how modern dynamical systems theory can help us both in understanding the evolution of cosmological models, and in relating them to real cosmological observations. It will be an invaluable reference for graduate students and researchers in relativity, cosmology and dynamical systems theory.

Dynamical And Complex Systems

Dynamical And Complex Systems
Author: Bullett Shaun,Fearn Tom,Smith Frank
Pages: 228
ISBN: 9781786341051
Available:
Release: 2016-12-22
Editor: World Scientific
Language: en

Explanation of the Book:

This book leads readers from a basic foundation to an advanced level understanding of dynamical and complex systems. It is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as applied dynamical systems, Lotka–Volterra dynamical systems, applied dynamical systems theory, dynamical systems in cosmology, aperiodic order, and complex systems dynamics. Dynamical and Complex Systems is the fifth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Editor the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

Dynamical Systems in Cosmology and Astrophysics

Dynamical Systems in Cosmology and Astrophysics
Author: Ulf Nilsson
Pages: 62
ISBN: 9171537899
Available:
Release: 1998
Editor: Unknown
Language: en

Explanation of the Book:

Dynamical Systems in Cosmology

Dynamical Systems in Cosmology
Author: N. Chan
Pages: 329
ISBN: OCLC:829960096
Available:
Release: 2012
Editor: Unknown
Language: en

Explanation of the Book:

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.

Introduction To General Relativity And Cosmology

Introduction To General Relativity And Cosmology
Author: Christian G Boehmer
Pages: 288
ISBN: 9781786341204
Available:
Release: 2016-10-06
Editor: World Scientific Publishing Company
Language: en

Explanation of the Book:

Introduction to General Relativity and Cosmology gives undergraduate students an overview of the fundamental ideas behind the geometric theory of gravitation and spacetime. Through pointers on how to modify and generalise Einstein's theory to enhance understanding, it provides a link between standard textbook content and current research in the field.Chapters present complicated material practically and concisely, initially dealing with the mathematical foundations of the theory of relativity, in particular differential geometry. This is followed by a discussion of the Einstein field equations and their various properties. Also given is analysis of the important Schwarzschild solutions, followed by application of general relativity to cosmology. Questions with fully worked answers are provided at the end of each chapter to aid comprehension and guide learning. This pared down textbook is specifically designed for new students looking for a workable, simple presentation of some of the key theories in modern physics and mathematics.

Order and Chaos in Dynamical Astronomy

Order and Chaos in Dynamical Astronomy
Author: George Contopoulos
Pages: 624
ISBN: 9783662049174
Available:
Release: 2013-03-14
Editor: Springer Science & Business Media
Language: en

Explanation of the Book:

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.

Dynamical Systems and Spherically Symmetric Cosmological Models

Dynamical Systems and Spherically Symmetric Cosmological Models
Author: Yanjing He
Pages: 586
ISBN: 0494166835
Available:
Release: 2006
Editor: Unknown
Language: en

Explanation of the Book:

Primordial Cosmology

Primordial Cosmology
Author: Anonim
Pages: 329
ISBN: 9789814468336
Available:
Release: 2021
Editor: Unknown
Language: en

Explanation of the Book:

Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics

Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics
Author: Oleg Igorevich Bogoi︠a︡vlenskiĭ
Pages: 301
ISBN: UCAL:$B526518
Available:
Release: 1985
Editor: Springer Verlag
Language: en

Explanation of the Book:

Cantorian Space time Dynamical Systems and Applications in Cosmology

Cantorian Space time  Dynamical Systems and Applications in Cosmology
Author: Gerardo Iovane
Pages: 329
ISBN: OCLC:1045898846
Available:
Release: 2004
Editor: Unknown
Language: en

Explanation of the Book:

Dynamical Systems in Social Psychology

Dynamical Systems in Social Psychology
Author: Robin R. Vallacher,Andrzej Nowak
Pages: 305
ISBN: UOM:39015032766100
Available:
Release: 1994-01-25
Editor: Academic Press
Language: en

Explanation of the Book:

A dynamical system refers to a set of elements that interact in complex, often nonlinear ways to form coherent patterns. Because of the complexity of these interactions, the system as a whole may evolve over time in seemingly unpredictable ways as new patterns of behavior emerge. This metatheory has proven useful in understanding diverse phenomena in meteorology, population biology, statistical mechanics, economics, and cosmology. The book demonstrates how the dynamical systems perspective can be applied to theory construction and research in social psychology, and in doing so, provides fresh insight into such complex phenomena as interpersonal behavior, social relations, attitudes, and social cognition.

Physical Foundations of Cosmology

Physical Foundations of Cosmology
Author: Viatcheslav Mukhanov
Pages: 329
ISBN: 9781139447119
Available:
Release: 2005-11-10
Editor: Cambridge University Press
Language: en

Explanation of the Book:

Inflationary cosmology has been developed over the last twenty years to remedy serious shortcomings in the standard hot big bang model of the universe. This textbook, first published in 2005, explains the basis of modern cosmology and shows where the theoretical results come from. The book is divided into two parts; the first deals with the homogeneous and isotropic model of the Universe, the second part discusses how inhomogeneities can explain its structure. Established material such as the inflation and quantum cosmological perturbation are presented in great detail, however the reader is brought to the frontiers of current cosmological research by the discussion of more speculative ideas. An ideal textbook for both advanced students of physics and astrophysics, all of the necessary background material is included in every chapter and no prior knowledge of general relativity and quantum field theory is assumed.

Cosmological Dynamical Systems

Cosmological Dynamical Systems
Author: Genly Leon
Pages: 385
ISBN: 3847302337
Available:
Release: 2012-01-19
Editor: LAP Lambert Academic Publishing
Language: en

Explanation of the Book:

Over the last century, the investigations in Gravitation and Cosmology have attracted the attention of thousand of human minds. Apart this boom in popularity, the homework task for cosmologists is to try to give an answer to the reasons why the present Universe has the properties that are observed. In spite of having a well-established theoretical framework like the Einstein's gravity theory (GR), which is valid in an amplest rank of energies and that has responded satisfactorily to numerous empirical verifications, are numerous unanswered intriguing questions. Is the dark energy the cause of the acceleration of the expansion? What is its equation of state nowadays? Why the energy densities of matter and dark energy of the same order of magnitude nowadays? Will be the acceleration of the expansion an indication that the action of Einstein-Hilbert must be modified? Can be reached the isotropic degree of the universe that is observed today, independently of the initial degree of anisotropy? In this book are studied, from the perspective of the dynamical systems, several Universe models that try to give answers to some of these questions.

Dynamical Systems Approach to Turbulence

Dynamical Systems Approach to Turbulence
Author: Tomas Bohr,Mogens H. Jensen,Angelo Vulpiani,Giovanni Paladin
Pages: 350
ISBN: 9780521475143
Available:
Release: 1998-08-13
Editor: Cambridge University Press
Language: en

Explanation of the Book:

This book treats turbulence from the point of view of dynamical systems. In recent decades, turbulence has evolved into a very active field of theoretical physics. The modern theory of fractals and multifractals now plays a major role in turbulence research, and turbulent states are being studied as important dynamical states of matter, in a much broader context than hydrodynamics. The origin of this development is the approach to turbulence from the point of view of deterministic dynamical systems, and in this book it is shown how concepts developed for low dimensional chaotic systems can be applied to turbulent states.

A Dynamical Systems Approach to Relativistic Stars and Cosmology

A Dynamical Systems Approach to Relativistic Stars and Cosmology
Author: Niklas Röhr
Pages: 59
ISBN: 918533510X
Available:
Release: 2004
Editor: Unknown
Language: en

Explanation of the Book:

A Dynamical Systems Theory of Thermodynamics

A Dynamical Systems Theory of Thermodynamics
Author: Wassim M. Haddad
Pages: 744
ISBN: 9780691190143
Available:
Release: 2019-06-04
Editor: Princeton University Press
Language: en

Explanation of the Book:

A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics. This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics. A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe—the entropic arrow of time.

Canonical Gravity and Applications

Canonical Gravity and Applications
Author: Martin Bojowald
Pages: 329
ISBN: 9781139494137
Available:
Release: 2010-12-23
Editor: Cambridge University Press
Language: en

Explanation of the Book:

Canonical methods are a powerful mathematical tool within the field of gravitational research, both theoretical and experimental, and have contributed to a number of recent developments in physics. Providing mathematical foundations as well as physical applications, this is the first systematic explanation of canonical methods in gravity. The book discusses the mathematical and geometrical notions underlying canonical tools, highlighting their applications in all aspects of gravitational research from advanced mathematical foundations to modern applications in cosmology and black hole physics. The main canonical formulations, including the Arnowitt-Deser-Misner (ADM) formalism and Ashtekar variables, are derived and discussed. Ideal for both graduate students and researchers, this book provides a link between standard introductions to general relativity and advanced expositions of black hole physics, theoretical cosmology or quantum gravity.

Relativistic Cosmology

Relativistic Cosmology
Author: George F. R. Ellis,Roy Maartens,Malcolm A. H. MacCallum
Pages: 329
ISBN: 9781139642958
Available:
Release: 2012-03-22
Editor: Cambridge University Press
Language: en

Explanation of the Book:

Cosmology has been transformed by dramatic progress in high-precision observations and theoretical modelling. This book surveys key developments and open issues for graduate students and researchers. Using a relativistic geometric approach, it focuses on the general concepts and relations that underpin the standard model of the Universe. Part I covers foundations of relativistic cosmology whilst Part II develops the dynamical and observational relations for all models of the Universe based on general relativity. Part III focuses on the standard model of cosmology, including inflation, dark matter, dark energy, perturbation theory, the cosmic microwave background, structure formation and gravitational lensing. It also examines modified gravity and inhomogeneity as possible alternatives to dark energy. Anisotropic and inhomogeneous models are described in Part IV, and Part V reviews deeper issues, such as quantum cosmology, the start of the universe and the multiverse proposal. Colour versions of some figures are available at www.cambridge.org/9780521381154.

Teleparallel Gravity

Teleparallel Gravity
Author: Ruben Aldrovandi,Jose G Pereira
Pages: 214
ISBN: 9789400751439
Available:
Release: 2012-08-10
Editor: Springer Science & Business Media
Language: en

Explanation of the Book:

Teleparallel Gravity (TG) is an alternative theory for gravitation, which is equivalent to General Relativity (GR). However, it is conceptually different. For example in GR geometry replaces the concept of force, and the trajectories are determined by geodesics. TG attributes gravitation to torsion, which accounts for gravitation by acting as a force. TG has already solved some old problems of gravitation (like the energy-momentum density of the gravitational field). The interest in TG has grown in the last few years. The book here proposed will be the first one dedicated exclusively to TG, and will include the foundations of the theory, as well as applications to specific problems to illustrate how the theory works.