Download or read book Quasi Periodic Motions in Families of Dynamical Systems written by Hendrik W. Broer and published by Springer. This book was released on 2009-01-25 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the phenomenon of quasi-periodic motion in dynamical systems. Such a motion in the phase space densely fills up an invariant torus. This phenomenon is most familiar from Hamiltonian dynamics. Hamiltonian systems are well known for their use in modelling the dynamics related to frictionless mechanics, including the planetary and lunar motions. In this context the general picture appears to be as follows. On the one hand, Hamiltonian systems occur that are in complete order: these are the integrable systems where all motion is confined to invariant tori. On the other hand, systems exist that are entirely chaotic on each energy level. In between we know systems that, being sufficiently small perturbations of integrable ones, exhibit coexistence of order (invariant tori carrying quasi-periodic dynamics) and chaos (the so called stochastic layers). The Kolmogorov-Arnol'd-Moser (KAM) theory on quasi-periodic motions tells us that the occurrence of such motions is open within the class of all Hamiltonian systems: in other words, it is a phenomenon persistent under small Hamiltonian perturbations. Moreover, generally, for any such system the union of quasi-periodic tori in the phase space is a nowhere dense set of positive Lebesgue measure, a so called Cantor family. This fact implies that open classes of Hamiltonian systems exist that are not ergodic. The main aim of the book is to study the changes in this picture when other classes of systems - or contexts - are considered.
Download or read book Quasi Periodic Motions in Families of Dynamical Systems written by Hendrik W. Broer and published by . This book was released on 2014-01-15 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 Global Analysis of Dynamical Systems written by H.W Broer and published by CRC Press. This book was released on 2001-06-18 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributed by close colleagues, friends, and former students of Floris Takens, Global Analysis of Dynamical Systems is a liber amicorum dedicated to Takens for his 60th birthday. The first chapter is a reproduction of Takens's 1974 paper "Forced oscillators and bifurcations" that was previously available only as a preprint of the University of Utrecht. Among other important results, it contains the unfolding of what is now known as the Bogdanov-Takens bifurcation. The remaining chapters cover topics as diverse as bifurcation theory, Hamiltonian mechanics, homoclinic bifurcations, routes to chaos, ergodic theory, renormalization theory, and time series analysis. In its entirety, the book bears witness to the influence of Takens on the modern theory of dynamical systems and its applications. This book is a must-read for anyone interested in this active and exciting field.
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 Averaging Methods in Nonlinear Dynamical Systems written by Jan A. Sanders and published by Springer Science & Business Media. This book was released on 2007-08-18 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with illuminating diagrams.
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 and Small Divisors written by Hakan Eliasson and published by Springer. This book was released on 2004-10-11 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems of stability in the theory of dynamical systems face the difficulty of small divisors. The most famous example is probably given by Kolmogorov-Arnold-Moser theory in the context of Hamiltonian systems, with many applications to physics and astronomy. Other natural small divisor problems arise considering circle diffeomorphisms or quasiperiodic Schroedinger operators. In this volume Hakan Eliasson, Sergei Kuksin and Jean-Christophe Yoccoz illustrate the most recent developments of this theory both in finite and infinite dimension. A list of open problems (including some problems contributed by John Mather and Michel Herman) has been included.
Download or read book New Frontiers of Celestial Mechanics Theory and Applications written by Giulio Baù and published by Springer Nature. This book was released on 2023-02-09 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the detailed text of the major lectures delivered during the I-CELMECH Training School 2020 held in Milan (Italy). The school aimed to present a contemporary review of recent results in the field of celestial mechanics, with special emphasis on theoretical aspects. The stability of the Solar System, the rotations of celestial bodies and orbit determination, as well as the novel scientific needs raised by the discovery of exoplanetary systems, the management of the space debris problem and the modern space mission design are some of the fundamental problems in the modern developments of celestial mechanics. This book covers different topics, such as Hamiltonian normal forms, the three-body problem, the Euler (or two-centre) problem, conservative and dissipative standard maps and spin-orbit problems, rotational dynamics of extended bodies, Arnold diffusion, orbit determination, space debris, Fast Lyapunov Indicators (FLI), transit orbits and answer to a crucial question, how did Kepler discover his celebrated laws? Thus, the book is a valuable resource for graduate students and researchers in the field of celestial mechanics and aerospace engineering.
Download or read book The KAM Story written by H Scott Dumas and published by World Scientific Publishing Company. This book was released on 2014-02-28 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science. The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a “breakthrough”). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory). Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.
Download or read book Hamiltonian Systems with Three or More Degrees of Freedom written by Carles Simó and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 681 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics. The Hamiltonian systems appearing in most of the applications are non-integrable. Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed. For systems near an integrable one, it can be shown that, under suitable conditions, some parts of the integrable structure, most of the invariant tori, survive. Many of the papers discuss near-integrable systems. From a topological point of view, some singularities must appear in different problems, either caustics, geodesics, moving wavefronts, etc. This is also related to singularities in the projections of invariant objects, and can be used as a signature of these objects. Hyperbolic dynamics appear as a source on unpredictable behaviour and several mechanisms of hyperbolicity are presented. The destruction of tori leads to Aubrey-Mather objects, and this is touched on for a related class of systems. Examples without periodic orbits are constructed, against a classical conjecture. Other topics concern higher dimensional systems, either finite (networks and localised vibrations on them) or infinite, like the quasiperiodic Schrödinger operator or nonlinear hyperbolic PDE displaying quasiperiodic solutions. Most of the applications presented concern celestial mechanics problems, like the asteroid problem, the design of spacecraft orbits, and methods to compute periodic solutions.
Download or read book Dynamics Stochastics written by Michael S. Keane and published by IMS. This book was released on 2006 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Differential Equations and Applications written by Fernando Casas and published by Springer. This book was released on 2014-11-05 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains a selection of contributions given at the 23th Congress on Differential Equations and Applications (CEDYA) / 13th Congress of Applied Mathematics (CMA) that took place at Castellon, Spain, in 2013. CEDYA is renowned as the congress of the Spanish Society of Applied Mathematics (SEMA) and constitutes the main forum and meeting point for applied mathematicians in Spain. The papers included in this book have been selected after a thorough refereeing process and provide a good summary of the recent activity developed by different groups working mainly in Spain on applications of mathematics to several fields of science and technology. The purpose is to provide a useful reference of academic and industrial researchers working in the area of numerical analysis and its applications.
Download or read book New Advances in Celestial Mechanics and Hamiltonian Systems written by Joaquín Delgado and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the IV International Symposium on Hamiltonian Systems and Celestial Mechanics, HAMSYS-2001 was to join top researchers in the area of Celestial Mechanics, Hamiltonian systems and related topics in order to communicate new results and look forward for join research projects. For PhD students, this meeting offered also the opportunity of personal contact to help themselves in their own research, to call as well and promote the attention of young researchers and graduated students from our scientific community to the above topics, which are nowadays of interest and relevance in Celestial Mechanics and Hamiltonian dynamics. A glance to the achievements in the area in the last century came as a consequence of joint discussions in the workshop sessions, new problems were presented and lines of future research were delineated. Specific discussion topics included: New periodic orbits and choreographies in the n-body problem, singularities in few body problems, central configurations, restricted three body problem, geometrical mechanics, dynamics of charged problems, area preserving maps and Arnold diffusion.
Download or read book Essays in Mathematics and its Applications written by Themistocles M. Rassias and published by Springer. This book was released on 2016-06-14 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to the eminent mathematician Vladimir Arnold, presents a collection of research and survey papers written on a large spectrum of theories and problems that have been studied or introduced by Arnold himself. Emphasis is given to topics relating to dynamical systems, stability of integrable systems, algebraic and differential topology, global analysis, singularity theory and classical mechanics. A number of applications of Arnold’s groundbreaking work are presented. This publication will assist graduate students and research mathematicians in acquiring an in-depth understanding and insight into a wide domain of research of an interdisciplinary nature.
Download or read book A Toolbox of Averaging Theorems written by Ferdinand Verhulst and published by Springer Nature. This book was released on 2023-08-23 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer on averaging theorems provides a practical toolbox for applied mathematicians, physicists, and engineers seeking to apply the well-known mathematical theory to real-world problems. With a focus on practical applications, the book introduces new approaches to dissipative and Hamiltonian resonances and approximations on timescales longer than 1/ε. Accessible and clearly written, the book includes numerous examples ranging from elementary to complex, making it an excellent basic reference for anyone interested in the subject. The prerequisites have been kept to a minimum, requiring only a working knowledge of calculus and ordinary and partial differential equations (ODEs and PDEs). In addition to serving as a valuable reference for practitioners, the book could also be used as a reading guide for a mathematics seminar on averaging methods. Whether you're an engineer, scientist, or mathematician, this book offers a wealth of practical tools and theoretical insights to help you tackle a range of mathematical problems.
