Author: Jurgen Moser
Publisher: Princeton University Press
ISBN: 1400882699
Category : Science
Languages : en
Pages : 216
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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.
Author: Jürgen Moser
Publisher:
ISBN:
Category : Celestial mechanics
Languages : en
Pages : 198
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Book Description
The Description for this book, Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics. (AM-77), will be forthcoming.
Author: G. B. Folland
Publisher:
ISBN: 9780691081120
Category : Algebraic number theory
Languages : en
Pages : 198
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Book Description
Author: Jurgen Moser
Publisher: American Mathematical Soc.
ISBN: 0821835777
Category : Combinatorial dynamics
Languages : en
Pages : 266
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Book Description
This book is an introduction to the field of dynamical systems, in particular, to the special class of Hamiltonian systems. The authors aimed at keeping the requirements of mathematical techniques minimal but giving detailed proofs and many examples and illustrations from physics and celestial mechanics. After all, the celestial $N$-body problem is the origin of dynamical systems and gave rise in the past to many mathematical developments. Jurgen Moser (1928-1999) was a professor atthe Courant Institute, New York, and then at ETH Zurich. He served as president of the International Mathematical Union and received many honors and prizes, among them the Wolf Prize in mathematics. Jurgen Moser is the author of several books, among them Stable and Random Motions in DynamicalSystems. Eduard Zehnder is a professor at ETH Zurich. He is coauthor with Helmut Hofer of the book Symplectic Invariants and Hamiltonian Dynamics. Information for our distributors: Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Author: A.A. Martynyuk
Publisher: CRC Press
ISBN: 1439876878
Category : Mathematics
Languages : en
Pages : 310
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Book Description
This self-contained book provides systematic instructive analysis of uncertain systems of the following types: ordinary differential equations, impulsive equations, equations on time scales, singularly perturbed differential equations, and set differential equations. Each chapter contains new conditions of stability of unperturbed motion of the abo
Author: Yuri Kifer
Publisher: Springer Science & Business Media
ISBN: 1461581818
Category : Mathematics
Languages : en
Pages : 301
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Book Description
Mathematicians often face the question to which extent mathematical models describe processes of the real world. These models are derived from experimental data, hence they describe real phenomena only approximately. Thus a mathematical approach must begin with choosing properties which are not very sensitive to small changes in the model, and so may be viewed as properties of the real process. In particular, this concerns real processes which can be described by means of ordinary differential equations. By this reason different notions of stability played an important role in the qualitative theory of ordinary differential equations commonly known nowdays as the theory of dynamical systems. Since physical processes are usually affected by an enormous number of small external fluctuations whose resulting action would be natural to consider as random, the stability of dynamical systems with respect to random perturbations comes into the picture. There are differences between the study of stability properties of single trajectories, i. e. , the Lyapunov stability, and the global stability of dynamical systems. The stochastic Lyapunov stability was dealt with in Hasminskii [Has]. In this book we are concerned mainly with questions of global stability in the presence of noise which can be described as recovering parameters of dynamical systems from the study of their random perturbations. The parameters which is possible to obtain in this way can be considered as stable under random perturbations, and so having physical sense. -1- Our set up is the following.
Author: Archie E. Roy
Publisher: Springer Science & Business Media
ISBN: 146845997X
Category : Science
Languages : en
Pages : 581
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Book Description
The reader will find in this volume the Proceedings of the NATO Advanced Study Institute held in Cortina d'Ampezzo, Italy between August 6 and August 17, 1990 under the title "Predictability, Stability, and Chaos in N-Body Dynamical Systems". The Institute was the latest in a series held at three-yearly inter vals from 1972 to 1987 in dynamical astronomy, theoretical mechanics and celestial mechanics. These previous institutes, held in high esteem by the international community of research workers, have resulted in a series of well-received Proceedings. The 1990 Institute attracted 74 participants from 16 countries, six outside the NATO group. Fifteen series of lectures were given by invited speakers; additionally some 40 valuable presentations were made by the younger participants, most of which are included in these Proceedings. The last twenty years in particular has been a time of increasingly rapid progress in tackling long-standing and also newly-arising problems in dynamics of N-body systems, point-mass and non-point-mass, a rate of progress achieved because of correspondingly rapid developments of new computer hardware and software together with the advent of new analytical techniques. It was a time of exciting progress culminating in the ability to carry out research programmes into the evolution of the outer Solar 8 System over periods of more than 10 years and to study star cluster and galactic models in unprecedented detail.
Author: Princeton University Press Staff
Publisher: Princeton University Press
ISBN: 0691238170
Category : Language Arts & Disciplines
Languages : en
Pages : 192
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Book Description
It all began atop a drugstore in Princeton, New Jersey, in November 1905. From its modest beginnings, Princeton University Press was to become one of the world's most important scholarly publishers, embracing a wealth of disciplines that have enriched our cultural, academic, and scientific landscape. Both as a tribute to our authors and to celebrate our centenary, Princeton University Press here presents A Century in Books. This beautifully designed volume highlights 100 of the nearly 8,000 books we have published. Necessarily winnowed from a much larger list, these books best typify what has been most lasting, most defining, and most distinctive about our publishing history--from Einstein's The Meaning of Relativity (1922) to the numerous mathematical and other works that marked the Press's watershed decade of the 1940s, including von Neumann and Morgenstern's Theory of Games and Economic Behavior; from milestones of literary criticism by Erich Auerbach and Northop Frye to George Kennan's Pulitzer Prize-winning book on Soviet-American relations; from Milton Friedman and Anna Jacobson Schwartz's A Monetary History of the United States, 1867-1960 to more recent landmarks such as L. Luca Cavalli-Sforza, Paolo Menozzi, and Alberto Piazza's The History and Geography of Human Genes and Robert Shiller's Irrational Exuberance. In addition to succinct descriptions of the 100 titles and a short introduction on the history of the Press, the book features five essays by prominent scholars and writers: Michael Wood discusses the impact on Princeton University Press of intellectuals who fled Nazi Germany and authored many influential books. Anthony Grafton recounts our rich publishing tradition in history, politics, and culture. Sylvia Nasar traces our evolution into a leading voice in economics publishing. Daniel Kevles reflects on Einstein, a figure of special importance to Princeton. And Lord Robert May writes on our long-standing tradition of publishing in mathematics and science. A Century in Books is more than a celebration of 100 years of publishing at Princeton University Press--it is a treasure trove of 100 years of books that have added to the richness of twentieth-century intellectual life.
Author: A. S. Wightman
Publisher: Springer Science & Business Media
ISBN: 1468412213
Category : Science
Languages : en
Pages : 312
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Book Description
The fifth International School ~ Mathematical Physics was held at the Ettore Majorana Centro della Culture Scientifica, Erice, Sicily, 2 to 14 July 1983. The present volume collects lecture notes on the session which was devoted to'Regular and Chaotic Motions in Dynamlcal Systems. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research and the Regional Sicilian Government. Many of the fundamental problems of this subject go back to Poincare and have been recognized in recent years as being of basic importance in a variety of physical contexts: stability of orbits in accelerators, and in plasma and galactic dynamics, occurrence of chaotic motions in the excitations of solids, etc. This period of intense interest on the part of physicists followed nearly a half a century of neglect in which research in the subject was almost entirely carried out by mathematicians. It is an in dication of the difficulty of some of the problems involved that even after a century we do not have anything like a satisfactory solution.
Author: V.G. Szebehely
Publisher: Springer Science & Business Media
ISBN: 9400998090
Category : Science
Languages : en
Pages : 361
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Book Description
P. J. MESSAGE University of Liverpool The papers which comprise this volume were presented at Colloquium No. 41 of the International Astronimical Union, which was held in Cambridge, England, from the 17th to the 19th of August, 1976, and had as its subject 'Dynamics of Planets and Satellites and Theories of their Motion'. The Colloquium was held just prior to the XVIth General Assembly of the Union (which was held from 24th August to 2nd September, in Grenoble, France) to provide an opportunity for the presentation of research papers on a number of active and lively branches of Celestial Mechanics to a gathering of experts in the field, and for the stimulus of discussion of research problems of interest to participants. A number of papers testify to the progress being made in General Planetary Theory, the theories of motion of the minor planets, the Moon, and the satellites of Jupiter and Saturn, and to significant advances in both the general and restricted gravitational problems of three bodies. The Organizing Committee of the Colloquium was comprised of J. Chapront, R. L. Duncombe, J. Hadjidemetriou, Y. Kozai, B. Morando, J. Schubart, V. Szebehely, and P. J. Message (Chairman). The local Organizer was D. C. Heggie, to whose tireless efforts the success of the arrangements is due. IX LIST OF PARTICIPANTS N. Abu-el-Ata, Bureau des Longitudes, 77 Avenue Denfert Rochereau, 75014 Paris, France K. Aksnes, Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, U. S. A.
