Download or read book Stable and Random Motions in Dynamical Systems written by Jurgen Moser and published by Princeton University Press. This book was released on 2016-03-02 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stable and Random Motions in Dynamical Systems with Special Emphasis on Celestial Mechanics written by Jürgen Moser and published by . This book was released on 1973 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Description for this book, Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics. (AM-77), will be forthcoming.
Download or read book Stable and Random Motions in Dynamical Systems with Special Emphasis on Celestial Mechanics written by G. B. Folland and published by . This book was released on 1973 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Notes on Dynamical Systems written by Jurgen Moser and published by American Mathematical Soc.. This book was released on 2005 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Uncertain Dynamical Systems written by A.A. Martynyuk and published by CRC Press. This book was released on 2011-11-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Random Perturbations of Dynamical Systems written by Yuri Kifer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Regular and Chaotic Motions in Dynamic Systems written by A. S. Wightman and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Predictability Stability and Chaos in N Body Dynamical Systems written by Archie E. Roy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Century in Books written by Princeton University Press Staff and published by Princeton University Press. This book was released on 2021-10-12 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Dynamics of Planets and Satellites and Theories of Their Motion written by V.G. Szebehely and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Feynman Integral and Random Dynamics in Quantum Physics written by Z. Haba and published by Springer Science & Business Media. This book was released on 2013-03-11 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Feynman integral is considered as an intuitive representation of quantum mechanics showing the complex quantum phenomena in a language comprehensible at a classical level. It suggests that the quantum transition amplitude arises from classical mechanics by an average over various interfering paths. The classical picture suggested by the Feynman integral may be illusory. By most physicists the path integral is usually treated as a convenient formal mathematical tool for a quick derivation of useful approximations in quantum mechanics. Results obtained in the formalism of Feynman integrals receive a mathematical justification by means of other (usually much harder) methods. In such a case the rigour is achieved at the cost of losing the intuitive classical insight. The aim of this book is to formulate a mathematical theory of the Feynman integral literally in the way it was expressed by Feynman, at the cost of complexifying the configuration space. In such a case the Feynman integral can be expressed by a probability measure. The equations of quantum mechanics can be formulated as equations of random classical mechanics on a complex configuration space. The opportunity of computer simulations shows an immediate advantage of such a formulation. A mathematical formulation of the Feynman integral should not be considered solely as an academic question of mathematical rigour in theoretical physics.
Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Download or read book Dynamical Systems written by Clark Robinson and published by CRC Press. This book was released on 1998-11-17 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several distinctive aspects make Dynamical Systems unique, including: treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas through examples and at a level accessible to a beginning graduate student
Download or read book Handbook of Dynamical Systems written by H. Broer and published by Elsevier. This book was released on 2010-11-10 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems
Download or read book An Exploration of Dynamical Systems and Chaos written by John H. Argyris and published by Springer. This book was released on 2015-04-24 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is conceived as a comprehensive and detailed text-book on non-linear dynamical systems with particular emphasis on the exploration of chaotic phenomena. The self-contained introductory presentation is addressed both to those who wish to study the physics of chaotic systems and non-linear dynamics intensively as well as those who are curious to learn more about the fascinating world of chaotic phenomena. Basic concepts like Poincaré section, iterated mappings, Hamiltonian chaos and KAM theory, strange attractors, fractal dimensions, Lyapunov exponents, bifurcation theory, self-similarity and renormalisation and transitions to chaos are thoroughly explained. To facilitate comprehension, mathematical concepts and tools are introduced in short sub-sections. The text is supported by numerous computer experiments and a multitude of graphical illustrations and colour plates emphasising the geometrical and topological characteristics of the underlying dynamics. This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures. "This book will be of valuable help for my lectures" Hermann Haken, Stuttgart "This text-book should not be missing in any introductory lecture on non-linear systems and deterministic chaos" Wolfgang Kinzel, Würzburg “This well written book represents a comprehensive treatise on dynamical systems. It may serve as reference book for the whole field of nonlinear and chaotic systems and reports in a unique way on scientific developments of recent decades as well as important applications.” Joachim Peinke, Institute of Physics, Carl-von-Ossietzky University Oldenburg, Germany
Download or read book Perspectives of Nonlinear Dynamics Volume 2 written by E. Atlee Jackson and published by CUP Archive. This book was released on 1989 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations.
Download or read book Geometric and Probabilistic Structures in Dynamics written by Keith Burns and published by American Mathematical Soc.. This book was released on 2008 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents a collection of articles that cover areas of mathematics related to dynamical systems. The authors are well-known experts who use geometric and probabilistic methods to study interesting problems in the theory of dynamical systems and its applications. Some of the articles are surveys while others are original contributions. The topics covered include: Riemannian geometry, models in mathematical physics and mathematical biology, symbolic dynamics, random and stochastic dynamics. This book can be used by graduate students and researchers in dynamical systems and its applications."--BOOK JACKET.
