Renormalisation In Area Preserving Maps
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| Author | : R. S. MacKay |
| Publisher | : World Scientific |
| Total Pages | : 332 |
| Release | : 1993 |
| Genre | : Mathematics |
| ISBN | : 9789810213718 |
This book is adapted and revised from the author's seminal PhD thesis, in which two forms of asymptotically universal structure were presented and explained for area-preserving maps. Area-preserving maps are the discrete-time analogue of two degree-of-freedom Hamiltonian systems. How they work and much of their dynamics are described in this book. The asymptotically universal structure is found on small scales in phase-space and long time-scales. The key to understanding it is renormalisation, that is, looking at a system on successively smaller phase-space and longer time scales. Having presented this idea, the author briefly surveys the use of the idea of renormalisation in physics. The renormalisation picture is then presented as the key to understanding the transition from regular to chaotic motion in area-preserving maps. Although written ten years ago, the subject matter continues to interest many today. This updated version will be useful to both researchers and students.
| Author | : Robert S Mackay |
| Publisher | : World Scientific |
| Total Pages | : 327 |
| Release | : 1993-08-31 |
| Genre | : Science |
| ISBN | : 9814504300 |
This book is adapted and revised from the author's seminal PhD thesis, in which two forms of asymptotically universal structure were presented and explained for area-preserving maps. Area-preserving maps are the discrete-time analogue of two degree-of-freedom Hamiltonian systems. How they work and much of their dynamics are described in this book. The asymptotically universal structure is found on small scales in phase-space and long time-scales. The key to understanding it is renormalisation, that is, looking at a system on successively smaller phase-space and longer time scales. Having presented this idea, the author briefly surveys the use of the idea of renormalisation in physics. The renormalisation picture is then presented as the key to understanding the transition from regular to chaotic motion in area-preserving maps. Although written ten years ago, the subject matter continues to interest many today. This updated version will be useful to both researchers and students.
| Author | : Robert Sinclair Mackay |
| Publisher | : |
| Total Pages | : |
| Release | : 1986 |
| Genre | : |
| ISBN | : |
| Author | : R.S MacKay |
| Publisher | : CRC Press |
| Total Pages | : 797 |
| Release | : 2020-08-17 |
| Genre | : Mathematics |
| ISBN | : 100011208X |
Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.
| Author | : Michael V. Berry |
| Publisher | : Princeton University Press |
| Total Pages | : 209 |
| Release | : 2014-07-14 |
| Genre | : Science |
| ISBN | : 1400860199 |
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 | : B.A. Steves |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 640 |
| Release | : 1998-12-31 |
| Genre | : Science |
| ISBN | : 9780792354666 |
Proceedings of the NATO Advanced Study Institute, Maratea, Italy, 29 June-12 July 1997
| Author | : Daniel Benest |
| Publisher | : CRC Press |
| Total Pages | : 334 |
| Release | : 1998-10-28 |
| Genre | : Computers |
| ISBN | : 9789056996253 |
The theory of dynamical systems, or mappings, plays an important role in various disciplines of modern physics, including celestial mechanics and fluid mechanics. This comprehensive introduction to the general study of mappings has particular emphasis on their applications to the dynamics of the solar system. The book forms a bridge between continuous systems, which are suited to analytical developments and to discrete systems, which are suitable for numerical exploration. Featuring chapters based on lectures delivered at the School on Discrete Dynamical Systems (Aussois, France, February 1996) the book contains three parts - Numerical Tools and Modelling, Analytical Methods, and Examples of Application. It provides a single source of information that, until now, has been available only in widely dispersed journal articles.
| Author | : Mikhail Lyubich |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 412 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821871560 |
Schwarzian derivatives and cylinder maps by A. Bonifant and J. Milnor Holomorphic dynamics: Symbolic dynamics and self-similar groups by V. Nekrashevych Are there critical points on the boundaries of mother hedgehogs? by D. K. Childers Finiteness for degenerate polynomials by L. DeMarco Cantor webs in the parameter and dynamical planes of rational maps by R. L. Devaney Simple proofs of uniformization theorems by A. A. Glutsyuk The Yoccoz combinatorial analytic invariant by C. L. Petersen and P. Roesch Bifurcation loci of exponential maps and quadratic polynomials: Local connectivity, triviality of fibers, and density of hyperbolicity by L. Rempe and D. Schleicher Rational and transcendental Newton maps by J. Ruckert Newton's method as a dynamical system: Efficient root finding of polynomials and the Riemann $\zeta$ function by D. Schleicher The external boundary of $M_2$ by V. Timorin Renormalization: Renormalization of vector fields by H. Koch Renormalization of arbitrary weak noises for one-dimensional critical dynamical systems: Summary of results and numerical explorations by O. Diaz-Espinosa and R. de la Llave KAM for the nonlinear Schrodinger equation--A short presentation by H. L. Eliasson and S. B. Kuksin Siegel disks and renormalization fixed points by M. Yampolsky
| Author | : T. Bedford |
| Publisher | : Cambridge University Press |
| Total Pages | : 301 |
| Release | : 1988-02-11 |
| Genre | : Mathematics |
| ISBN | : 0521348803 |
This book comprises a collection of survey articles that review the state of progress in several different areas of research into dynamical systems theory. Each paper is intended to provide both an overview of a specific area and an introduction of new ideas and techniques.
| Author | : Arun V. Holden |
| Publisher | : Princeton University Press |
| Total Pages | : 333 |
| Release | : 2014-07-14 |
| Genre | : Science |
| ISBN | : 1400858151 |
This volume sets out the basic applied mathematical and numerical methods of chaotic dynamics and illustrates the wide range of phenomena, inside and outside the laboratory, that can be treated as chaotic processes. Originally published in 1986. 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.
