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Author: G. Haller
Publisher: Springer Science & Business Media
ISBN: 1461215080
Category : Mathematics
Languages : en
Pages : 444
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Book Description
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of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds.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.
Author: G. Haller
Publisher: Springer Science & Business Media
ISBN: 1461215080
Category : Mathematics
Languages : en
Pages : 444
Get Book Here
Book Description
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of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds.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.
Author: Wanda Szemplinska-stupnicka
Publisher: World Scientific
ISBN: 981448363X
Category : Technology & Engineering
Languages : en
Pages : 117
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Book Description
During the last twenty years, a large number of books on nonlinear chaotic dynamics in deterministic dynamical systems have appeared. These academic tomes are intended for graduate students and require a deep knowledge of comprehensive, advanced mathematics. There is a need for a book that is accessible to general readers, a book that makes it possible to get a good deal of knowledge about complex chaotic phenomena in nonlinear oscillators without deep mathematical study.Chaos, Bifurcations and Fractals Around Us: A Brief Introduction fills that gap. It is a very short monograph that, owing to geometric interpretation complete with computer color graphics, makes it easy to understand even very complex advanced concepts of chaotic dynamics. This invaluable publication is also addressed to lecturers in engineering departments who want to include selected nonlinear problems in full time courses on general mechanics, vibrations or physics so as to encourage their students to conduct further study.
Author: Sadrilla Abdullaev
Publisher: Springer Science & Business Media
ISBN: 3319018906
Category : Science
Languages : en
Pages : 422
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Book Description
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.
Author: Carles Simó
Publisher: Springer Science & Business Media
ISBN: 940114673X
Category : Mathematics
Languages : en
Pages : 681
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Book Description
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.
Author: George Contopoulos
Publisher: Springer Science & Business Media
ISBN: 3662049171
Category : Science
Languages : en
Pages : 633
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Book Description
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.
Author: Michael V. Berry
Publisher: Princeton University Press
ISBN: 1400860199
Category : Science
Languages : en
Pages : 209
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Book Description
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.
Author: Sylvio Ferraz-Mello
Publisher: Springer Science & Business Media
ISBN: 9780792317821
Category : Science
Languages : en
Pages : 432
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Book Description
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.
Author: Denis Makarov
Publisher: World Scientific
ISBN: 981427318X
Category : Science
Languages : en
Pages : 412
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Book Description
1. Ray and wave propagation. 1.1. Underwater sound channel. 1.2. Basic equations. 1.3. Geometrical optics approximations and optical-mechanical analogy. The Hamiltonian formalism. 1.4. Ray travel times. 1.5. Range-dependent environments. 1.6. Acoustic ocean tomography. 1.7. Experiments on long-range sound propagation. 1.8. Summary -- 2. Ray chaos. 2.1. Hamiltonian chaos. 2.2. Lyapunov instability. 2.3. Ray-medium resonance. 2.4. Overlapping of resonances. 2.5. Vertical resonance. 2.6. Manifestation of regular and chaotic ray motion in distributions of ray travel times. 2.7. Summary -- 3. Wave chaos. 3.1. The problem of wave chaos. 3.2. Normal modes. 3.3. Mode coupling under chaotic conditions. 3.4. Influence of fine-scale inhomogeneities on wave dynamics. 3.5. Summary -- 4. Chaotic phenomena in random environment. 4.1. Ray chaos in a random medium. 4.2. Travel times of chaotic rays. 4.3. Modal structure of the sound field in a waveguide with random inhomogeneities. 4.4. Wave beam in an ocean acoustic waveguide. 4.5. Arrival times of sound pulses in the presence of internal waves and a mesoscale inhomogeneity. 4.6. Summary -- 5. Glossary of some concepts and notations in Hamiltonian chaos theory
Author: Kenju Otsuka
Publisher: Springer Science & Business Media
ISBN: 9780792361329
Category : Technology & Engineering
Languages : en
Pages : 326
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Book Description
This book is the first comprehensive volume on nonlinear dynamics and chaos in optical systems. A few books have been published recently, but they summarize applied mathematical methodologies toward understanding of nonlinear dynamics in laser systems with small degrees of freedom focusing on linearized perturbation and bifurcation analyses. In contrast to these publications, this book summarizes nonlinear dynamic problems in optical complex systems possessing large degrees of freedom, systematically featuring our original experimental results and their theoretical treatments. The new concepts introduced in this book will have a wide appeal to audiences involved in a rapidly-growing field of nonlinear dynamics. This book focuses on nonlinear dynamics and cooperative functions in realistic optical complex systems, such as multimode lasers, laser array, coupled nonlinear-element systems, and their applications to optical processing. This book is prepared for graduate students majoring in optical and laser physics, but the generic nature of complex systems described in this book may stimulate researchers in the field of nonlinear dynamics covering different academic areas including applied mathematics, hydrodynamics, celestial mechanics, chemistry, biology, and economics.
Author: Mikito Toda
Publisher: John Wiley & Sons
ISBN: 0471714631
Category : Science
Languages : en
Pages : 711
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Book Description
This series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. Volume 130 in the series continues to report recent advances with significant, up-to-date chapters by internationally recognized researchers.
