Chaos In Astronomy
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Order And Chaos In Dynamical Astronomy
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Author : George Contopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
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 2013-03-14 with Science categories.
There have been many books on Dynamical Astronomy up to now. Many are devoted to Celestial Mechanics, but there are also several books on Stellar and Galactic Dynamics. The first books on stellar dynamics dealt mainly with the statistics of stellar motions (e. g. Smart's "Stellar Dynamics" (1938), or Trumpler and Weaver's "Statistical Astronomy" (1953)). A classical book in this field is Chandrasekhar's "Principles of Stellar Dynamics" (1942) that dealt mainly with the time of relaxation, the solutions of Liouville's equation, and the dynamics of clusters. In the Dover edition of this book (1960) an extended Appendix was added, containing the statistical mechanics of stellar systems, a quite "modern" subject at that time. The need for a classroom book was covered for several years by the book of Mihalas and Routly "Galactic Astronomy" (1969). But the most complete book in this field is Binney and Tremaine's "Galactic Dynamics" (1987). This book covers well the classical topics of stellar dynamics, and many subjects of current interest. Another classical book in dynamical astronomy is the extensive 4-Volume treatise of Hagihara "Celestial Mechanics" (1970, 1972, 1974, 1975). In more recent years much progress has been made on new topics that are of vital interest for stellar and galactic dynamics. The main new topic is Chaos. The progress of the theory of chaos has influenced considerably the area of stellar and galactic dynamics. The study of order and chaos has provided a new dimension in dynamics.
Chaos In Astronomy
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Author : G. Contopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-01-07
Chaos In Astronomy written by G. 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 2009-01-07 with Science categories.
The conference 'Chaos in Astronomy' was held in Athens on 17-20 Sept. 2007. This book contains edited refereed contributions. It offers an overview to students and newcomers entering various fields of dynamical astronomy.
Stability And Chaos In Celestial Mechanics
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Author : Alessandra Celletti
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-10
Stability And Chaos In Celestial Mechanics written by Alessandra Celletti 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 2010-03-10 with Science categories.
This overview of classical celestial mechanics focuses the interplay with dynamical systems. Paradigmatic models introduce key concepts – order, chaos, invariant curves and cantori – followed by the investigation of dynamical systems with numerical methods.
Capture Dynamics And Chaotic Motions In Celestial Mechanics
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Author : Edward Belbruno
language : en
Publisher: Princeton University Press
Release Date : 2004
Capture Dynamics And Chaotic Motions In Celestial Mechanics written by Edward Belbruno and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Newton S Clock
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Author : Ivars Peterson
language : en
Publisher: Macmillan
Release Date : 1993
Newton S Clock written by Ivars Peterson and has been published by Macmillan this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Science categories.
With his critically acclaimed best-sellers The Mathematical Tourism and Islands of Truth, Ivars Peterson took readers to the frontiers of modern mathematics. His new book provides an up-to-date look at one of science's greatest detective stories: the search for order in the workings of the solar system. In the late 1600s, Sir Isaac Newton provided what astronomers had long sought: a seemingly reliable way of calculating planetary orbits and positions. Newton's laws of motion and his coherent, mathematical view of the universe dominated scientific discourse for centuries. At the same time, observers recorded subtle, unexpected movements of the planets and other bodies, suggesting that the solar system is not as placid and predictable as its venerable clock work image suggests. Today, scientists can go beyond the hand calculations, mathematical tables, and massive observational logs that limited the explorations of Newton, Copernicus, Galileo, Kepler, Tycho Brahe, and others. Using supercomputers to simulate the dynamics of the solar system, modern astronomers are learning more about the motions they observe and uncovering some astonishing examples of chaotic behavior in the heavens. Nonetheless, the long-term stability of the solar system remains a perplexing, unsolved issue, with each step toward its resolution exposing additional uncertainties and deeper mysteries. To show how our view of the solar system has changed from clocklike precision to chaos and complexity, Newton's Clock describes the development of celestial mechanics through the ages - from the star charts of ancient navigators to the seminal discoveries of the 17th century from the crucial work of Poincare to thestartling, sometimes controversial findings and theories made possible by modern mathematics and computer simulations. The result makes for entertaining and provocative reading, equal parts science, history and intellectual adventure.
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.
Chaos And Gauge Field Theory
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Author : T. S. Bir¢
language : en
Publisher: World Scientific
Release Date : 1994
Chaos And Gauge Field Theory written by T. S. Bir¢ and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
This book introduces a rapidly growing new research area ? the study of dynamical properties of elementary fields. The methods used in this field range from algebraic topology to parallel computer programming. The main aim of this research is to understand the behavior of elementary particles and fields under extreme circumstances, first of all at high temperature and energy density generated in the largest accelerators of the world and supposed to be present in the early evolution of our Universe shortly after the Big Bang.In particular, chaos is rediscovered in a new appearance in these studies: in gauge theories the well-known divergence of initially adjacent phase space trajectories leads over into a quasi-thermal distribution of energy with a saturated average distance of different field configurations. This particular behavior is due to the compactness of the gauge group.Generally this book is divided into two main parts: the first part mainly deals with the ?classical? discovery of chaos in gauge field theory while the second part presents methods and research achievements in recent years. One chapter is devoted entirely to the presentation and discussion of computational problems. The major theme, returning again and again throughout the book, is of course the phenomenon with a thousand faces ? chaos itself.This book is intended to be a research book which introduces the reader to a new research field, presenting the basic new ideas in detail but just briefly touching on the problems of other related fields, like perturbative or lattice gauge theory, or dissipative chaos. The terminology of these related fields are, however, used.Exercises are also included in this book. They deepen the reader's understanding of special issues and at the same time offer more information on related problems. For the convenience of the fast reader, solutions are presented right after the problems.
Quantum Signatures Of Chaos
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Author : Fritz Haake
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Quantum Signatures Of Chaos written by Fritz Haake 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 2013-03-09 with Science categories.
The warm reception of the first edition, as well as the tumultuous development of the field of quantum chaos have tempted me to rewrite this book and include some of the important progress made during the past decade. Now we know that quantum signatures of chaos are paralleled by wave signa tures. Whatever is undergoing wavy space-time variations, be it sound, electro magnetism, or quantum amplitudes, each shows exactly the same manifestations of chaos. The common origin is nonseparability of the pertinent wave equation; that latter "definition" of chaos, incidentally, also applies to classical mechanics if we see the Hamilton-Jacobi equation as the limiting case of a wave equation. At any rate, drums, concert halls, oscillating quartz blocks, microwave and opti cal oscillators, electrons moving ballistically or with impurity scattering through mesoscopic devices all provide evidence and data for wave or quantum chaos. All of these systems have deep analogies with billiards, much as the latter may have appeared of no more than academic interest only a decade ago. Of course, molec ular, atomic, and nuclear spectroscopy also remain witnesses of chaos, while the chromodynamic innards of nucleons are beginning to attract interest as methods of treatment become available.
Chaos From Simple Models To Complex Systems
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Author : Angelo Vulpiani
language : en
Publisher: World Scientific
Release Date : 2009-09-01
Chaos From Simple Models To Complex Systems written by Angelo Vulpiani and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-01 with Mathematics categories.
Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theory and applications encompassing fluid and celestial mechanics, chemistry and biology.The book is novel in devoting attention to a few topics often overlooked in introductory textbooks and which are usually found only in advanced surveys such as: information and algorithmic complexity theory applied to chaos and generalization of Lyapunov exponents to account for spatiotemporal and non-infinitesimal perturbations.The selection of topics, numerous illustrations, exercises and proposals for computer experiments make the book ideal for both introductory and advanced courses.
Chaos Unveiled
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Author : Barrett Williams
language : en
Publisher: Barrett Williams
Release Date : 2024-08-21
Chaos Unveiled written by Barrett Williams and has been published by Barrett Williams this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-21 with Mathematics categories.
**Chaos Unveiled An Expedition into the Intricate World of Chaos Theory and Complex Systems** Unlock the mysteries of the universe's most captivating phenomenon with "Chaos Unveiled," an enlightening journey through chaos theory and complex systems. Crafted to engross and educate, this book serves as your definitive guide to understanding the unpredictable nature of the world around us. Dive into **Chapter 1** and explore the humble beginnings of chaos theory and its dramatic evolution into a pivotal scientific discipline. Discover key contributors and the milestones that have defined this groundbreaking field. Move into **Chapter 2**, where the intricate mathematics behind chaos comes to life. Understand nonlinear dynamics, sensitivity to initial conditions, and the enigmatic strange attractors that lead to seemingly random behaviors out of deterministic processes. In **Chapter 3**, delve into the mesmerizing world of fractals and self-similarity. From the beauty of fractal geometry to real-world applications, this chapter is a visual and intellectual feast. **Chapter 4** takes you into fluid dynamics, demystifying the complex phenomena of turbulence, vortices, and the iconic Lorenz attractor that revolutionized weather prediction and modeling. Explore the fascinating roles chaos plays in **biological systems** in **Chapter 5**, from population dynamics and cardiac rhythms to intricate ecosystems and food webs. Unravel the secrets of chaotic behavior in chemical reactions in **Chapter 6**, and discover how these principles govern both simple reactions and the complex chemistry of living organisms. Venture into **economic chaos** in **Chapter 7**, understanding stock market fluctuations, market bubbles, and the unpredictable nature of economic forecasting. The applications of chaos theory in **engineering** are unlocked in **Chapter 8**, revealing insights into control systems, structural analysis, and the ever-evolving field of robotics and machine learning. **Chapter 9** sheds light on chaos in social systems, from human behavior and social networks to the intricacies of urban planning. Experience medical breakthroughs in **Chapter 10**, where chaos theory enhances diagnostics, epidemiology, and our understanding of brain activity. Discover chaos in the vast expanse of **environmental science** and **astronomy** in **Chapters 11 and 12**, exploring climate change, earthquake prediction, orbital mechanics, and cosmic phenomena. **Chapter 13** provides groundbreaking insights into computational approaches, from numerical simulations to data analysis and pattern recognition. Reflect on the **philosophical implications** in **Chapter 14** as you weigh determinism against randomness and ponder the ethical considerations of predictability. Finally, look towards the **future of chaos theory** in **Chapter 15**, exploring emerging research areas, interdisciplinary collaborations, and the bright horizon of unanswered questions and challenges. "Chaos Unveiled" is not merely a book—it's an invitation to explore, question, and understand the beautifully intricate world of chaos theory. Get ready to have your mind expanded and your curiosity ignited!