Download or read book Chaos Near Resonance written by G. Haller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.
Download or read book Order and Chaos in Dynamical Astronomy written by George Contopoulos and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Chaos Resonance and Collective Dynamical Phenomena in the Solar System written by Sylvio Ferraz-Mello and published by Springer Science & Business Media. This book was released on 1992-05-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Resonance And Bifurcation To Chaos In Pendulum written by Luo Albert C J and published by World Scientific. This book was released on 2017-12-15 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system. This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum. Contents: Resonance and Hamiltonian ChaosHamiltonian Chaos in PendulumParametric Chaos in PendulumNonlinear Discrete SystemsPeriodic Flows in Continuous SystemsPeriodic Motions to Chaos in Pendulum Readership: Researchers and academics in the field of mathematics. Keywords: Mathematics;Resonance: Bifurcation;Chaos in Pendulum;Nonlinear Science, Chaos & Dynamical SystemsReview:0
Download or read book Global Transversality Resonance and Chaotic Dynamics written by Albert C. J. Luo and published by World Scientific. This book was released on 2008 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n -dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics. Sample Chapter(s). Chapter 1: Introduction (1,196 KB). Contents: Differential Geometry of Flows; Global Transversality in Continuous Dynamical Systems; Chaotic Layer Dynamics; Two-Dimensional Stochastic Layers; Stochasticity in Resonant Separatrix Layers; Nonlinear Dynamics on an Equi-energy Surface; Stability and Grazing in Dissipative Systems; Global Dynamics in Two-Dimensional Dynamical Systems; Flow Switchability in Discontinuous Dynamical Systems. Readership: Mathematicians, physicists, researchers and engineers in mechanical engineering and electrical engineering as well as university professors and students.
Download or read book Dynamical Chaos written by Michael V. Berry and published by Princeton University Press. This book was released on 2014-07-14 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leading scientists who gave these papers under the sponsorship of the Royal Society in early 1987 provide reviews of facets of the subject of chaos ranging from the practical aspects of mirror machines for fusion power to the pure mathematics of geodesics on surfaces of negative curvature. The papers deal with systems in which chaotic conditions arise from initial value problems with unique solutions, as opposed to those where chaos is produced by the introduction of noise from an external source. Table of Contents Diagnosis of Dynamical Systems with Fluctuating Parameters D. Ruelle Nonlinear Dynamics, Chaos, and Complex Cardiac Arrhythmias L. Glass, A. L. Goldberger, M. Courtemanche, and A. Shrier Chaos and the Dynamics of Biological Populations R. M. May Fractal Bifurcation Sets, Renormalization Strange Sets, and Their Universal Invariants D. A. Rand From Chaos to Turbulence in Bnard Convection A. Libchaber Dynamics of Convection N. O. Weiss Chaos: A Mixed Metaphor for Turbulence E. A. Spiegel Arithmetical Theory of Anosov Diffeomorphisms F. Vivaldi Chaotic Behavior in the Solar System J. Wisdom Chaos in Hamiltonian Systems I. C. Percival Semi-Classical Quantization, Adiabatic Invariants, and Classical Chaos W. P. Reinhardt and I. Dana Particle Confinement and Adiabatic Invariance B. V. Chirikov Some Geometrical Models of Chaotic Dynamics C. Series The Bakerian Lecture: Quantum Chaology M. V. Berry Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
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 Chaos in Astronomy written by G. Contopoulos and published by Springer Science & Business Media. This book was released on 2009-01-07 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Control of Homoclinic Chaos by Weak Periodic Perturbations written by Ricardo Chacón and published by World Scientific. This book was released on 2005-11-21 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a reasonably rigorous theory of a highly relevant chaos control method: suppression–enhancement of chaos by weak periodic excitations in low-dimensional, dissipative and non-autonomous systems. The theory provides analytical estimates of the ranges of parameters of the chaos-controlling excitation for suppression–enhancement of the initial chaos. The important applications of the theory presented in the book include: (1) control of chaotic escape from a potential well; (2) suppression of chaos in a driven Josephson junction; (3) control of chaotic solitons in Frenkel–Kontorova chains; (4) control of chaotic breather dynamics in perturbed sine-Gordon equations; (5) control of chaotic charged particles in electrostatic wave packets. Contents:Theoretical ApproachPhysical MechanismsApplications: Low-Dimensional SystemsApplications: High-Dimensional SystemsFurther Remarks and Open Problems Readership: Graduate students and researchers in physics, mathematics, chemistry and biology, as well as electrical, electronic, mechanical systems and control engineering. Keywords:Reviews:“This is a very interesting book with many nice examples of controlling chaos by means of analytical as well as numerical methods. It is well written, so it is suitable for and recommended to anyone who is interested in chaos and its control in nonlinear dynamical systems.”Mathematical Reviews
Download or read book Handbook of Accelerator Physics and Engineering written by Alex Chao and published by World Scientific. This book was released on 1999 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited by internationally recognized authorities in the field, this handbook focuses on Linacs, Synchrotrons and Storage Rings and is intended as a vade mecum for professional engineers and physicists engaged in these subjects. Here one will find, in addition to the common formulae of previous compilations, hard to find specialized formulae, recipes and material data pooled from the lifetime experiences of many of the world's most able practitioners of the art and science of accelerator building and operation.
Download or read book Quantum Chaos Y2K written by Karl-Fredrik Berggren and published by World Scientific. This book was released on 2001-10-09 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum chaos is becoming a very wide field that ranges from experiments to theoretical physics and purely mathematical issues. In view of this grand span, Nobel Symposium 116 focused on experiments and theory, and attempted to encourage interplay between them. There was emphasis on the interdisciplinary character of the subject, involving a broad range of subjects in physics, including condensed matter physics, nuclear physics, atomic physics and elementary particle physics. The physics involved in quantum chaos has much in common with acoustics, microwaves, optics, etc., and therefore the symposium also covered aspects of wave chaos in this broader sense. The program was structured according to the following areas: manifestations of classical chaos in quantum systems; transport phenomena; quantal spectra in terms of periodic orbits; semiclassical and random matrix approaches; quantum chaos in interacting systems; chaos and tunneling; wave-dynamic chaos. This important book constitutes the proceedings of the symposium. Contents: After-Dinner Speech (M C Gutzwiller)Spectral Twinkling: A New Example of Singularity-Dominated Strong Fluctuations (Summary) (M Berry)Ground State Spin and Coulomb Blockade Peak Motion in Chaotic Quantum Dots (J A Folk et al.)Quantum Chaos and Transport Phenomena in Quantum Dots (A S Sachrajda)Chaos in Quantum Ratchets (H Linke et al.)Non-Universality of Chaotic Classical Dynamics: Implications for Quantum Chaos (M Wilkinson)Chaos and Interactions in Quantum Dots (Y Alhassid)Stochastic Aspects of Many-Body Systems: The Embedded Gaussian Ensembles (H A Weidenmüller)Effect of Symmetry Breaking on Statistical Distributions (G E Mitchell & J F Shriner, Jr.)Quantum Chaos and Quantum Computers (D L Shepelyansky)Disorder and Quantum Chromodynamics — Non-Linear σ Models (T Guhr & T Wilke)Correlation Between Periodic Orbits and Their Rôle in Spectral Statistics (M Sieber & K Richter)Neutron Stars and Quantum Billiards (A Bulgac & P Magierski)Tunneling and Chaos (S Tomsovic)Relaxation and Fluctuations in Quantum Chaos (G Casati)Scars and Other Weak Localization Effects in Classically Chaotic Systems (E J Heller)Classically-Forbidden Processes in Photoabsorption Spectra (J B Delos et al.)Wave Dynamical Chaos: An Experimental Approach in Billiards (A Richter)Acoustic Chaos (C Ellegaard et al.)Wave-Chaotic Optical Resonators and Lasers (A D Stone)Angular Momentum Localization in Oval Billiards (J U Nöckel)Chaos and Time-Reversed Acoustics (M Fink)and other papers Readership: Quantum, nuclear, atomic, condensed matter and high energy physicists, as well as researchers in classical wave physics. Keywords:
Download or read book Applied Symbolic Dynamics and Chaos written by Bai-lin Hao and published by World Scientific. This book was released on 1998 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symbolic dynamics is a coarse-grained description of dynamics. It provides a rigorous way to understand the global systematics of periodic and chaotic motion in a system. In the last decade it has been applied to nonlinear systems described by one- and two-dimensional maps as well as by ordinary differential equations. This book will help practitioners in nonlinear science and engineering to master that powerful tool.
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 Mechanics written by Florian Scheck and published by Springer Science & Business Media. This book was released on 1999 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition closely follows the fifth German edition. In particular, it now contains an enlarged presentation of the "tippe top" and a new section on the use of Riemannian geometry in mechanics. As before, the book contains numerous problems with complete solutions, and some practical examples.This will be appreciated in particular by students using the text to accompnay lectures on mechanics. The main features of the book remain unchanged: the coverage extends from elementary Newtonian mechanics, Lagrangian as well as canonical Hamilton-Jacobian mechanics, the mechanics of rigid bodies, special relativity, and the geometric aspects of mechanics to the discussion of deterministic chaos and a short introduction to continuous systems. The book ends with some historical remarks on important pioneers in mechanics.
Download or read book Protostars and Planets VI written by Henrik Beuther and published by University of Arizona Press. This book was released on 2014-12-18 with total page 945 pages. Available in PDF, EPUB and Kindle. Book excerpt: The revolutionary discovery of thousands of confirmed and candidate planets beyond the solar system brings forth the most fundamental question: How do planets and their host stars form and evolve? Protostars and Planets VI brings together more than 250 contributing authors at the forefront of their field, conveying the latest results in this research area and establishing a new foundation for advancing our understanding of stellar and planetary formation. Continuing the tradition of the Protostars and Planets series, this latest volume uniquely integrates the cross-disciplinary aspects of this broad field. Covering an extremely wide range of scales, from the formation of large clouds in our Milky Way galaxy down to small chondrules in our solar system, Protostars and Planets VI takes an encompassing view with the goal of not only highlighting what we know but, most importantly, emphasizing the frontiers of what we do not know. As a vehicle for propelling forward new discoveries on stars, planets, and their origins, this latest volume in the Space Science Series is an indispensable resource for both current scientists and new students in astronomy, astrophysics, planetary science, and the study of meteorites.
Download or read book Introduction to Applied Nonlinear Dynamical Systems and Chaos written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2003-10-01 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to applied nonlinear dynamics and chaos places emphasis on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains a detailed glossary of terms. From the reviews: "Will serve as one of the most eminent introductions to the geometric theory of dynamical systems." --Monatshefte für Mathematik
Download or read book Chaos Concepts Control and Constructive Use written by Yurii Bolotin and published by Springer. This book was released on 2016-10-24 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interfaces of quantum physics and dynamical systems, examining in turn statistical properties of energy spectra, quantum ratchets, and dynamical tunneling, among others. This text is particularly suitable for non-specialist scientists, engineers, and applied mathematical scientists from related areas, wishing to enter the field quickly and efficiently. From the reviews of the first edition: This book is an excellent introduction to the key concepts and control of chaos in (random) dynamical systems [...] The authors find an outstanding balance between main physical ideas and mathematical terminology to reach their audience in an impressive and lucid manner. This book is ideal for anybody who would like to grasp quickly the main issues related to chaos in discrete and continuous time. Henri Schurz, Zentralblatt MATH, Vol. 1178, 2010.
