Dynamical And Complex Systems
Dynamical And Complex Systems

Author: Shaun Bullett

Publisher: World Scientific

Published: 2016-12-22

Total Pages: 228

ISBN-13: 1786341050

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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.

Dynamical Systems in Cosmology
Dynamical Systems in Cosmology

Author: J. Wainwright

Publisher: Cambridge University Press

Published: 1997-01-28

Total Pages: 361

ISBN-13: 0521554578

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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 Systems and Cosmology
Dynamical Systems and Cosmology

Author: A.A. Coley

Publisher: Springer Science & Business Media

Published: 2003-10-31

Total Pages: 210

ISBN-13: 9781402014031

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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.

Order and Chaos in Dynamical Astronomy
Order and Chaos in Dynamical Astronomy

Author: George Contopoulos

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 633

ISBN-13: 3662049171

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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.

Hamiltonian Dynamical Systems and Applications
Hamiltonian Dynamical Systems and Applications

Author: Walter Craig

Publisher: Springer Science & Business Media

Published: 2008-02-17

Total Pages: 450

ISBN-13: 1402069642

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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.

Stable and Random Motions in Dynamical Systems
Stable and Random Motions in Dynamical Systems

Author: Jurgen Moser

Publisher: Princeton University Press

Published: 2016-03-02

Total Pages: 216

ISBN-13: 1400882699

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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.

Beyond the Dynamical Universe
Beyond the Dynamical Universe

Author: Michael Silberstein

Publisher: Oxford University Press

Published: 2018-02-02

Total Pages: 445

ISBN-13: 0192533835

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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.

Relativistic Cosmology
Relativistic Cosmology

Author: George F. R. Ellis

Publisher: Cambridge University Press

Published: 2012-03-22

Total Pages: 637

ISBN-13: 0521381150

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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.

Primordial Cosmology
Primordial Cosmology

Author: Giovanni Montani

Publisher: World Scientific

Published: 2011-01-03

Total Pages: 617

ISBN-13: 9814468339

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Primordial Cosmology deals with one of the most puzzling and fascinating topics debated in modern physics — the nature of the Big Bang singularity. The authors provide a self-consistent and complete treatment of the very early Universe dynamics, passing through a concise discussion of the Standard Cosmological Model, a precise characterization of the role played by the theory of inflation, up to a detailed analysis of the anisotropic and inhomogeneous cosmological models. The most peculiar feature of this book is its uniqueness in treating advanced topics of quantum cosmology with a well-traced link to more canonical and pedagogical notions of fundamental cosmology.This book traces clearly the backward temporal evolution of the Universe, starting with the Robertson-Walker geometry and ending with the recent results of loop quantum cosmology in view of the Big Bounce. The reader is accompanied in this journey by an initial technical presentation which, thanks to the fundamental tools given earlier in the book, never seems heavy or obscure.

Dynamical Systems in Social Psychology
Dynamical Systems in Social Psychology

Author: Robin R. Vallacher

Publisher: Academic Press

Published: 1994-01-11

Total Pages: 338

ISBN-13:

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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.