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| Author | : G. Contopoulos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 493 |
| Release | : 2009-01-07 |
| Genre | : Science |
| ISBN | : 3540758267 |
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.
| Author | : George Contopoulos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 633 |
| Release | : 2013-03-14 |
| Genre | : 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 | : Ivars Peterson |
| Publisher | : Macmillan |
| Total Pages | : 341 |
| Release | : 1993 |
| Genre | : Science |
| ISBN | : 0716723964 |
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.
| Author | : Barry R. Parker |
| Publisher | : Springer |
| Total Pages | : 307 |
| Release | : 2013-11-11 |
| Genre | : Science |
| ISBN | : 1489933700 |
'he year was 1889. The French physicist-mathematician Henry T Poincare could not believe his eyes. He had worked for months on one of the most famous problems in science-the problem of three bodies moving around one another under mutual gravita tional attraction-and what he was seeing dismayed and trou bled him. Since Newton's time it had been assumed that the problem was solvable. All that was needed was a little ingenuity and considerable perseverance, but Poincare saw that this was not the case. Strange, unexplainable things happened when he delved into the problem; it was not solvable after all. Poincare was shocked and dismayed by the result-so disheartened he left the problem and went on to other things. What Poincare was seeing was the first glimpse of a phe nomenon we now call chaos. With his discovery the area lay dormant for almost 90 years. Not a single book was written about the phenomenon, and only a trickle of papers appeared. Then, about 1980 a resurgence of interest began, and thousands of papers appeared along with dozens of books. The new science of chaos was born and has attracted as much attention in recent years as breakthroughs in superconductivity and superstring theory.
| Author | : O. Regev |
| Publisher | : Cambridge University Press |
| Total Pages | : 492 |
| Release | : 2006-03-23 |
| Genre | : Mathematics |
| ISBN | : 9780521855341 |
A primer for researchers and graduate students; introduces and applies chaos techniques to specific astrophysical systems.
| Author | : Alessandra Celletti |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 265 |
| Release | : 2010-03-10 |
| Genre | : Science |
| ISBN | : 3540851461 |
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.
| Author | : Charalampos (Haris) Skokos |
| Publisher | : Springer |
| Total Pages | : 280 |
| Release | : 2016-03-04 |
| Genre | : Science |
| ISBN | : 3662484102 |
Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics. To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data. In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists. The book covers theoretical and computational aspects of traditional methods to calculate Lyapunov exponents, as well as of modern techniques like the Fast (FLI), the Orthogonal (OFLI) and the Relative (RLI) Lyapunov Indicators, the Mean Exponential Growth factor of Nearby Orbits (MEGNO), the Smaller (SALI) and the Generalized (GALI) Alignment Index and the ‘0-1’ test for chaos.
| Author | : Alexei Fridman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 140 |
| Release | : 2011-06-27 |
| Genre | : Science |
| ISBN | : 9401002479 |
On August 2000 in the Lomonosov Moscow State University the first scientific conference dedicated to chaos in the real astronomical systems was held. The most prominent astrophysisists - specialist in the field of stochastic dynamics - attended the conference. A broad scope of the problems related to the observed manifes tations of chaotic motions in galactic and stellar objects, with the involvement of basic theory and numerical modeling, were addressed. The idea (not so obvious, as we believe, to many astrophysicists) was to show that, while great progress in the field of stochastic mechanics was accomplished, the science of chaos in actually observed systems is only just being born. Basically, the situation described prompted the organizers to hold the meeting in order to discuss chaotic processes in real systems. It seemed worthwhile to begin these introductory remarks with a brief descrip tion of some events that preceeded the conference. Since actually existing systems are the subject of the natural sciences, and in the latter experiments play the key role, we shall begin our account with the experimental results.
| Author | : V. G. Gurzadyan |
| Publisher | : World Scientific |
| Total Pages | : 692 |
| Release | : 2000 |
| Genre | : Science |
| ISBN | : 9789810242558 |
This unique volume is a collection of papers on various problems in astrophysics and cosmology ? from planetary motion to the arrow of time ? that are closely linked by the common spirit, technique and methodology of chaos.
| Author | : Sylvio Ferraz-Mello |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 432 |
| Release | : 1992-05-31 |
| Genre | : Science |
| ISBN | : 9780792317821 |
This symposium was devoted to a new celestial mechanics whose aim has become the study of such `objects' as the planetary system, planetary rings, the asteroidal belt, meteor swarms, satellite systems, comet families, the zodiacal cloud, the preplanetary nebula, etc. When the three-body problem is considered instead of individual orbits we are, now, looking for the topology of extended regions of its phase space. This Symposium was one step in the effort to close the ties between two scientific families: the observationally-oriented scientists and the theoretically-oriented scientists.
