Order and Chaos in Dynamical Astronomy


Book Description

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.




Adventures in Order and Chaos


Book Description

The field of Order and Chaos had a remarkable expansion in the last 50 years. The main reason was the use of computers, and the development of new theoretical methods that we call now 'the theory of chaos'. The author describes this fascinating period in a relaxed and sometimes humorous autobiographical way. He relates his interactions with many people in dynamical astronomy and he quotes several anecdotes from these interactions. He refers also to his experiences when he served in various international positions, such as general secretary of the IAU and chairman of the journal Astronomy and Astrophysics. In recent years the theory of chaos has been extended to new areas, like relativity, cosmology and quantum mechanics and it continues expanding in almost all branches of physics. The book describes many important ideas in this field in a simple way. It refers also to problems of more general interest, like writing papers and giving lectures and the interaction of authors and referees. Finally it gives some useful prospects for the future of dynamical astronomy and related fields. George Contopoulos, PhD U.Athens1953; Professor of Astronomy U.Thessaloniki 1957-75; U.Athens 1975-96; Emeritus 1996-; Member, Academy of Athens 1997-. Visiting Professor Yale U., Harvard U., MIT, Cornell U., U.Chicago, U.Maryland, U. Florida, Florida State U., U. Milan; Res. Associate, Yerkes Obs., Inst.Adv.Study Princeton, Inst.Space Studies, Goddard Flight Center, Columbia U., ESO. Author or Editor of 15 books, and about 250 papers on Galactic Dynamics, Relativity and Celestial Mechanics. Positions held: Gen.Secretary of the IAU; Director General Nat.Obs.of Greece, Pres.Hellenic Astron.Soc.; Nat.Representative of Greece in NATO, etc. Distinctions: Amer. Astron.Soc. Brouwer Prize; U.Chicago, Honorary Doctor's Degree; IAU, Pres. Commission 33 (Galaxy); Member Academia Europaea; Associate Royal Astron. Soc.; Chairman of the European Journal "Astronomy and Astrophysics"; Assoc. Editor of "Cel. Mech. Dyn. Astron."; Over 4500 citations and 300 acknowledgements.




Adventures in Order and Chaos


Book Description

For many years I was organizing a weekly seminar on dynamical astronomy, and I used to make some historical remarks on every subject, including some anecdotes from my contacts with many leading scientists over the years. I described also the development of various subjects and the emergence of new ideasindynamicalastronomy. Thenseveralpeoplepromptedmetowritedown these remarks, which cannot be found in papers, or books. Thus, I decided to write this book, which contains my experiences over the years. I hope that this book may be helpful to astronomy students all over the world. During my many years of teaching, as a visiting professor, in American Universities (1962-1994, Yale, Harvard, MIT, Cornell, Chicago, Maryland and Florida) I was impressed by the quality of my graduate students. Most of them were very bright, asking penetrating questions, and preparing their homework in a perfect way. In a few cases, instead of a ?nal examination, I assigned to them some small research projects and they presented their results at the end of the course. They were excellent in preparing the appropriate slides and in presenting their results in a concise and clear way.




Chaos in Astronomy


Book Description

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


Book Description

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.




Chaos and Complexity in Astrophysics


Book Description

A primer for researchers and graduate students; introduces and applies chaos techniques to specific astrophysical systems.




From Chaos To Order: Methodologies, Perspectives And Applications


Book Description

Chaos control has become a fast-developing interdisciplinary research field in recent years. This book is for engineers and applied scientists who want to have a broad understanding of the emerging field of chaos control. It describes fundamental concepts, outlines representative techniques, provides case studies, and highlights recent developments, putting the reader at the forefront of current research.Important topics presented in the book include:




Stable and Random Motions in Dynamical Systems


Book Description

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.




Complexity


Book Description

“If you liked Chaos, you’ll love Complexity. Waldrop creates the most exciting intellectual adventure story of the year” (The Washington Post). In a rarified world of scientific research, a revolution has been brewing. Its activists are not anarchists, but rather Nobel Laureates in physics and economics and pony-tailed graduates, mathematicians, and computer scientists from all over the world. They have formed an iconoclastic think-tank and their radical idea is to create a new science: complexity. They want to know how a primordial soup of simple molecules managed to turn itself into the first living cell—and what the origin of life some four billion years ago can tell us about the process of technological innovation today. This book is their story—the story of how they have tried to forge what they like to call the science of the twenty-first century. “Lucidly shows physicists, biologists, computer scientists and economists swapping metaphors and reveling in the sense that epochal discoveries are just around the corner . . . [Waldrop] has a special talent for relaying the exhilaration of moments of intellectual insight.” —The New York Times Book Review “Where I enjoyed the book was when it dove into the actual question of complexity, talking about complex systems in economics, biology, genetics, computer modeling, and so on. Snippets of rare beauty here and there almost took your breath away.” —Medium “[Waldrop] provides a good grounding of what may indeed be the first flowering of a new science.” —Publishers Weekly




Surface Chaos and Its Applications


Book Description

This book addresses a special topic in the field of nonlinear dynamical systems, develops a new research direction of surface chaos and surface bifurcation. It provides a clear watershed for original nonlinear chaos and bifurcation research. The novel content of this book makes nonlinear system research more systematical and personalized. This book introduces the chaos and bifurcation behavior of surface dynamics in the sense of Li Yorke, the basic properties, Lyapunov exponent and Feigenbaum constant of nonlinear behavior of surface, and obtained the wave behavior of chaotic process in surface motion, the control of surface chaos and bifurcation, and the wide application of surface chaos in engineering technology. Through this book, readers can obtain more abundant and novel contents about surface chaos and surface bifurcation than the existing mixed fitting bifurcation of plane curve and space curve, which can also expand the realm and vision of research.