Author : J. Wainwright
Publisher : Cambridge University Press
Page : 361 pages
File Size : 44,76 MB
Release : 1997-01-28
Category : Mathematics
ISBN : 0521554578
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 : Shaun Bullett
Publisher : World Scientific
Page : 228 pages
File Size : 21,57 MB
Release : 2016-12-22
Category : Mathematics
ISBN : 1786341050
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. Edited by 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 : A.A. Coley
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 39,46 MB
Release : 2003-10-31
Category : Science
ISBN : 9781402014031
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 : A.A. Coley
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 10,46 MB
Release : 2013-04-17
Category : Science
ISBN : 9401703272
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 : George Contopoulos
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 47,36 MB
Release : 2013-03-14
Category : Science
ISBN : 3662049171
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 : Walter Craig
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 11,32 MB
Release : 2008-02-17
Category : Mathematics
ISBN : 1402069642
This volume is the collected and extended notes from the lectures on Hamiltonian dynamical systems and their applications that were given at the NATO Advanced Study Institute in Montreal in 2007. Many aspects of the modern theory of the subject were covered at this event, including low dimensional problems. Applications are also presented to several important areas of research, including problems in classical mechanics, continuum mechanics, and partial differential equations.
Author : Michael Silberstein
Publisher : Oxford University Press
Page : 445 pages
File Size : 48,16 MB
Release : 2018-02-02
Category : Science
ISBN : 0192533835
Theoretical physics and foundations of physics have not made much progress in the last few decades. Whether we are talking about unifying general relativity and quantum field theory (quantum gravity), explaining so-called dark energy and dark matter (cosmology), or the interpretation and implications of quantum mechanics and relativity, there is no consensus in sight. In addition, both enterprises are deeply puzzled about various facets of time including above all, time as experienced. The authors argue that, across the board, this impasse is the result of the "dynamical universe paradigm," the idea that reality is fundamentally made up of physical entities that evolve in time from some initial state according to dynamical laws. Thus, in the dynamical universe, the initial conditions plus the dynamical laws explain everything else going exclusively forward in time. In cosmology, for example, the initial conditions reside in the Big Bang and the dynamical law is supplied by general relativity. Accordingly, the present state of the universe is explained exclusively by its past. This book offers a completely new paradigm (called Relational Blockworld), whereby the past, present and future co-determine each other via "adynamical global constraints," such as the least action principle. Accordingly, the future is just as important for explaining the present as is the past. Most of the book is devoted to showing how Relational Blockworld resolves many of the current conundrums of both theoretical physics and foundations of physics, including the mystery of time as experienced and how that experience relates to the block universe.
Author : Jurgen Moser
Publisher : Princeton University Press
Page : 216 pages
File Size : 24,96 MB
Release : 2016-03-02
Category : Science
ISBN : 1400882699
For centuries, astronomers have been interested in the motions of the planets and in methods to calculate their orbits. Since Newton, mathematicians have been fascinated by the related N-body problem. They seek to find solutions to the equations of motion for N masspoints interacting with an inverse-square-law force and to determine whether there are quasi-periodic orbits or not. Attempts to answer such questions have led to the techniques of nonlinear dynamics and chaos theory. In this book, a classic work of modern applied mathematics, Jürgen Moser presents a succinct account of two pillars of the theory: stable and chaotic behavior. He discusses cases in which N-body motions are stable, covering topics such as Hamiltonian systems, the (Moser) twist theorem, and aspects of Kolmogorov-Arnold-Moser theory. He then explores chaotic orbits, exemplified in a restricted three-body problem, and describes the existence and importance of homoclinic points. This book is indispensable for mathematicians, physicists, and astronomers interested in the dynamics of few- and many-body systems and in fundamental ideas and methods for their analysis. After thirty years, Moser's lectures are still one of the best entrées to the fascinating worlds of order and chaos in dynamics.
Author : Carl D. Murray
Publisher : Cambridge University Press
Page : 612 pages
File Size : 16,66 MB
Release : 2000-02-13
Category : Science
ISBN : 1139936158
The Solar System is a complex and fascinating dynamical system. This is the first textbook to describe comprehensively the dynamical features of the Solar System and to provide students with all the mathematical tools and physical models they need to understand how it works. It is a benchmark publication in the field of planetary dynamics and destined to become a classic. Clearly written and well illustrated, Solar System Dynamics shows how a basic knowledge of the two- and three-body problems and perturbation theory can be combined to understand features as diverse as the tidal heating of Jupiter's moon Io, the origin of the Kirkwood gaps in the asteroid belt, and the radial structure of Saturn's rings. Problems at the end of each chapter and a free Internet Mathematica® software package are provided. Solar System Dynamics provides an authoritative textbook for courses on planetary dynamics and celestial mechanics. It also equips students with the mathematical tools to tackle broader courses on dynamics, dynamical systems, applications of chaos theory and non-linear dynamics.
Author : George F. R. Ellis
Publisher : Cambridge University Press
Page : 637 pages
File Size : 39,26 MB
Release : 2012-03-22
Category : Science
ISBN : 0521381150
Surveying key developments and open issues in cosmology for graduate students and researchers, this book focuses on the general concepts and relations that underpin the standard model of the Universe. It also examines anisotropic and inhomogeneous models, and deeper issues, such as quantum cosmology and the multiverse proposal.
