Chaos Near Resonance
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Chaos Near Resonance
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Author : G. Haller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Chaos Near Resonance written by G. Haller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds.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.
Resonance And Bifurcation To Chaos In Pendulum
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Author : Luo Albert C J
language : en
Publisher: World Scientific
Release Date : 2017-12-15
Resonance And Bifurcation To Chaos In Pendulum written by Luo Albert C J and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Science categories.
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
Chaos Resonance And Collective Dynamical Phenomena In The Solar System
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Author : Sylvio Ferraz-Mello
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-05-31
Chaos Resonance And Collective Dynamical Phenomena In The Solar System written by Sylvio Ferraz-Mello and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-31 with Science categories.
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.
Order And Chaos In Dynamical Astronomy
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Author : George Contopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Order And Chaos In Dynamical Astronomy written by George Contopoulos and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
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.
Global Transversality Resonance And Chaotic Dynamics
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Author : Albert C. J. Luo
language : en
Publisher: World Scientific
Release Date : 2008
Global Transversality Resonance And Chaotic Dynamics written by Albert C. J. Luo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
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.
Chaotic Dynamics And Transport In Classical And Quantum Systems
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Author : Pierre Collet
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-28
Chaotic Dynamics And Transport In Classical And Quantum Systems written by Pierre Collet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-07-28 with Science categories.
From the 18th to the 30th August 2003 , a NATO Advanced Study Institute (ASI) was held in Cargèse, Corsica, France. Cargèse is a nice small village situated by the mediterranean sea and the Institut d'Etudes Scientifiques de Cargese provides ? a traditional place to organize Theoretical Physics Summer Schools and Workshops * in a closed and well equiped place. The ASI was an International Summer School on "Chaotic Dynamics and Transport in Classical and Quantum Systems". The main goal of the school was to develop the mutual interaction between Physics and Mathematics concerning statistical properties of classical and quantum dynamical systems. Various experimental and numerical observations have shown new phenomena of chaotic and anomalous transport, fractal structures, chaos in physics accelerators and in cooled atoms inside atom-optics billiards, space-time chaos, fluctuations far from equilibrium, quantum decoherence etc. New theoretical methods have been developed in order to modelize and to understand these phenomena (volume preserving and ergodic dynamical systems, non-equilibrium statistical dynamics, fractional kinetics, coupled maps, space-time entropy, quantum dissipative processes etc). The school gathered a team of specialists from several horizons lecturing and discussing on the achievements, perspectives and open problems (both fundamental and applied).
Chaos Concepts Control And Constructive Use
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Author : Yurii Bolotin
language : en
Publisher: Springer
Release Date : 2016-10-24
Chaos Concepts Control And Constructive Use written by Yurii Bolotin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-24 with Science categories.
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.
Magnetic Stochasticity In Magnetically Confined Fusion Plasmas
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Author : Sadrilla Abdullaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-19
Magnetic Stochasticity In Magnetically Confined Fusion Plasmas written by Sadrilla Abdullaev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-19 with Science categories.
This is the first book to systematically consider the modern aspects of chaotic dynamics of magnetic field lines and charged particles in magnetically confined fusion plasmas. The analytical models describing the generic features of equilibrium magnetic fields and magnetic perturbations in modern fusion devices are presented. It describes mathematical and physical aspects of onset of chaos, generic properties of the structure of stochastic magnetic fields, transport of charged particles in tokamaks induced by magnetic perturbations, new aspects of particle turbulent transport, etc. The presentation is based on the classical and new unique mathematical tools of Hamiltonian dynamics, like the action--angle formalism, classical perturbation theory, canonical transformations of variables, symplectic mappings, the Poincaré-Melnikov integrals. They are extensively used for analytical studies as well as for numerical simulations of magnetic field lines, particle dynamics, their spatial structures and statistical properties. The numerous references to articles on the latest development in the area are provided. The book is intended for graduate students and researchers who interested in the modern problems of magnetic stochasticity in magnetically confined fusion plasmas. It is also useful for physicists and mathematicians interested in new methods of Hamiltonian dynamics and their applications.
Dynamical Chaos
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Author : Michael V. Berry
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
Dynamical Chaos written by Michael V. Berry and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Science categories.
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.
Hamiltonian Systems With Three Or More Degrees Of Freedom
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Author : Carles Simó
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hamiltonian Systems With Three Or More Degrees Of Freedom written by Carles Simó and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.