Dynamical Systems And Cosmology

Author : A.A. Coley
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 41,5 Mb
Release : 2013-04-17
Category : Science
ISBN : 9789401703277

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Dynamical Systems and Cosmology by A.A. Coley Pdf

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.

Author : J. Wainwright,G. F. R. Ellis
Publisher : Cambridge University Press
Page : 360 pages
File Size : 55,9 Mb
Release : 2005-06-30
Category : Science
ISBN : 0521673526

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Dynamical Systems in Cosmology by J. Wainwright,G. F. R. Ellis Pdf

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.

Author : J. Wainwright,G. F. R. Ellis
Publisher : Cambridge University Press
Page : 361 pages
File Size : 43,8 Mb
Release : 1997-01-28
Category : Mathematics
ISBN : 9780521554572

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Dynamical Systems in Cosmology by J. Wainwright,G. F. R. Ellis Pdf

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.

Author : Bullett Shaun,Fearn Tom,Smith Frank
Publisher : World Scientific
Page : 228 pages
File Size : 45,9 Mb
Release : 2016-12-22
Category : Mathematics
ISBN : 9781786341051

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Dynamical And Complex Systems by Bullett Shaun,Fearn Tom,Smith Frank Pdf

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.

Author : Ulf Nilsson
Publisher : Unknown
Page : 62 pages
File Size : 55,8 Mb
Release : 1998
Category : Astrophysics
ISBN : 9171537899

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Dynamical Systems in Cosmology and Astrophysics by Ulf Nilsson Pdf

Author : Oleg Igorevich Bogoi͡avlenskiĭ
Publisher : Springer
Page : 328 pages
File Size : 42,7 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:39015017167019

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Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics by Oleg Igorevich Bogoi͡avlenskiĭ Pdf

Author : George Contopoulos
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 52,9 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662049174

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Order and Chaos in Dynamical Astronomy by George Contopoulos Pdf

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.

Author : Spiros Cotsakis,Eleftherios Papantonopoulos
Publisher : Springer
Page : 480 pages
File Size : 43,9 Mb
Release : 2008-01-11
Category : Science
ISBN : 9783540480259

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Cosmological Crossroads by Spiros Cotsakis,Eleftherios Papantonopoulos Pdf

This book has grown out of lectures held at a summer school on cosmology, in response to an ever increasing need for an advanced textbook that addresses the needs of both postgraduate students and nonspecialist researchers from various disciplines ranging from mathematical physics to observational astrophysics. Bridging the gap between standard textbook material in cosmology and the forefront of research, this book also constitutes a modern source of reference for the experienced researcher in classical and quantum cosmology.

Author : J. Robert Buchler,Stephen T. Gottesman,Henry E. Kandrup
Publisher : Unknown
Page : 370 pages
File Size : 42,5 Mb
Release : 1998
Category : Science
ISBN : UVA:X004335628

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Nonlinear Dynamics and Chaos in Astrophysics by J. Robert Buchler,Stephen T. Gottesman,Henry E. Kandrup Pdf

Nonlinear dynamics and chaos pervade dynamical problems on all astrophysical scales, ranging from the sun and solar system to galaxies and cosmology. This volume, the 13th in a series devoted to problems in nonlinear astronomy and physics, presents the work of 18 senior scientists from around the world as well as that of several postdoctoral associates to honour their mentor and colleague George Contopoulos, a seminal figure in this area of astrophysical research. Some of the topics considered are plasma physics, accelerator dynamics, several formal problems in nonlinear dynamics and several applied to astronomical problems on cosmology, accretion phenomena, and the structure and evolution of galaxies.

Author : O.I. Bogoyavlensky
Publisher : Springer
Page : 0 pages
File Size : 48,5 Mb
Release : 1985
Category : Mathematics
ISBN : 3642616615

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Methods in the Qualitative Theory of Dynamical Systems in Astrophysics and Gas Dynamics by O.I. Bogoyavlensky Pdf

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.

Author : Archie E. Roy
Publisher : Springer Science & Business Media
Page : 581 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781468459975

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Predictability, Stability, and Chaos in N-Body Dynamical Systems by Archie E. Roy Pdf

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title "Predictability, Stability, and Chaos in N-Body Dynamical Systems". The Institute was the latest in a series held at three-yearly inter vals from 1972 to 1987 in dynamical astronomy, theoretical mechanics and celestial mechanics. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received Proceedings. The 1990 Institute attracted 74 participants from 16 countries, six outside the NATO group. Fifteen series of lectures were given by invited speakers; additionally some 40 valuable presentations were made by the younger participants, most of which are included in these Proceedings. The last twenty years in particular has been a time of increasingly rapid progress in tackling long-standing and also newly-arising problems in dynamics of N-body systems, point-mass and non-point-mass, a rate of progress achieved because of correspondingly rapid developments of new computer hardware and software together with the advent of new analytical techniques. It was a time of exciting progress culminating in the ability to carry out research programmes into the evolution of the outer Solar 8 System over periods of more than 10 years and to study star cluster and galactic models in unprecedented detail.

Author : Shaun Bullett,T. Fearn,Frank T. Smith
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 1786341042

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Dynamical and Complex Systems by Shaun Bullett,T. Fearn,Frank T. Smith Pdf

Author : Edward Belbruno
Publisher : Princeton University Press
Page : 128 pages
File Size : 45,8 Mb
Release : 2018-06-05
Category : Mathematics
ISBN : 9780691186436

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Capture Dynamics and Chaotic Motions in Celestial Mechanics by Edward Belbruno Pdf

This book describes a revolutionary new approach to determining low energy routes for spacecraft and comets by exploiting regions in space where motion is very sensitive (or chaotic). It also represents an ideal introductory text to celestial mechanics, dynamical systems, and dynamical astronomy. Bringing together wide-ranging research by others with his own original work, much of it new or previously unpublished, Edward Belbruno argues that regions supporting chaotic motions, termed weak stability boundaries, can be estimated. Although controversial until quite recently, this method was in fact first applied in 1991, when Belbruno used a new route developed from this theory to get a stray Japanese satellite back on course to the moon. This application provided a major verification of his theory, representing the first application of chaos to space travel. Since that time, the theory has been used in other space missions, and NASA is implementing new applications under Belbruno's direction. The use of invariant manifolds to find low energy orbits is another method here addressed. Recent work on estimating weak stability boundaries and related regions has also given mathematical insight into chaotic motion in the three-body problem. Belbruno further considers different capture and escape mechanisms, and resonance transitions. Providing a rigorous theoretical framework that incorporates both recent developments such as Aubrey-Mather theory and established fundamentals like Kolmogorov-Arnold-Moser theory, this book represents an indispensable resource for graduate students and researchers in the disciplines concerned as well as practitioners in fields such as aerospace engineering.

Author : Lawrence Perko
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468402490

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Differential Equations and Dynamical Systems by Lawrence Perko Pdf

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.

Author : Archie E. Roy,B.A. Steves
Publisher : Springer Science & Business Media
Page : 573 pages
File Size : 49,7 Mb
Release : 2013-06-29
Category : Science
ISBN : 9781489910851

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From Newton to Chaos by Archie E. Roy,B.A. Steves Pdf

The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d' Ampezzo, Italy, between July 25 and August 6, 1993, under the title From Newton to Chaos: Modem Techniques for Understanding and Coping With Chaos inN-Body Dynamical Systems. This institute was the latest in a series of meetings held every three years from 1972 to 1990 in dynamical astronomy, theoretical mechanics and celestial mechanics. The proceedings from these institutes have been well-received in the international community of research workers in these disciplines. The present institute was well attended with 15 series of lectures being given by invited speakers: in addition some 40 presentations were made by the other participants. The majority of these contributions are included in these proceedings. The all-pervading influence of chaos in dynamical systems (of even a few variables) has now been universally recognised by researchers, a recognition forced on us by our ability, using powerful computer hardware and software, to tackle dynamical problems that until twenty-five years ago were intractable. Doubtless it was felt by many that these new techniques provided a break-through in celestial mechanics and its related disciplines. And so they were.