Construction Of Mappings For Hamiltonian Systems And Their Applications
Download Construction Of Mappings For Hamiltonian Systems And Their Applications full books in PDF, epub, and Kindle. Read online free Construction Of Mappings For Hamiltonian Systems And Their Applications ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: Sadrilla S. Abdullaev |
Publisher |
: Springer |
Total Pages |
: 384 |
Release |
: 2006-08-02 |
ISBN-10 |
: 9783540334170 |
ISBN-13 |
: 3540334173 |
Rating |
: 4/5 (70 Downloads) |
Synopsis Construction of Mappings for Hamiltonian Systems and Their Applications by : Sadrilla S. Abdullaev
Based on the method of canonical transformation of variables and the classical perturbation theory, this innovative book treats the systematic theory of symplectic mappings for Hamiltonian systems and its application to the study of the dynamics and chaos of various physical problems described by Hamiltonian systems. It develops a new, mathematically-rigorous method to construct symplectic mappings which replaces the dynamics of continuous Hamiltonian systems by the discrete ones. Applications of the mapping methods encompass the chaos theory in non-twist and non-smooth dynamical systems, the structure and chaotic transport in the stochastic layer, the magnetic field lines in magnetically confinement devices of plasmas, ray dynamics in waveguides, etc. The book is intended for postgraduate students and researches, physicists and astronomers working in the areas of plasma physics, hydrodynamics, celestial mechanics, dynamical astronomy, and accelerator physics. It should also be useful for applied mathematicians involved in analytical and numerical studies of dynamical systems.
Author |
: Carles Simó |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 681 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9789401146739 |
ISBN-13 |
: 940114673X |
Rating |
: 4/5 (39 Downloads) |
Synopsis Hamiltonian Systems with Three or More Degrees of Freedom by : Carles Simó
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 |
: Richard McGehee |
Publisher |
: Springer |
Total Pages |
: 224 |
Release |
: 1992 |
ISBN-10 |
: UOM:39015021523231 |
ISBN-13 |
: |
Rating |
: 4/5 (31 Downloads) |
Synopsis Twist Mappings and Their Applications by : Richard McGehee
Author |
: Jürgen Moser |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 92 |
Release |
: 1968 |
ISBN-10 |
: 9780821812815 |
ISBN-13 |
: 0821812815 |
Rating |
: 4/5 (15 Downloads) |
Synopsis Lectures on Hamiltonian Systems by : Jürgen Moser
Author |
: Stephen Lynch |
Publisher |
: Birkhäuser |
Total Pages |
: 590 |
Release |
: 2017-10-12 |
ISBN-10 |
: 9783319614854 |
ISBN-13 |
: 3319614851 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Dynamical Systems with Applications Using Mathematica® by : Stephen Lynch
This book provides an introduction to the theory of dynamical systems with the aid of the Mathematica® computer algebra package. The book has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Theorems and proofs are kept to a minimum. The first section deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems.
Author |
: Juan-Pablo Ortega |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 526 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9781475738117 |
ISBN-13 |
: 1475738110 |
Rating |
: 4/5 (17 Downloads) |
Synopsis Momentum Maps and Hamiltonian Reduction by : Juan-Pablo Ortega
* Winner of the Ferran Sunyer i Balaguer Prize in 2000. * Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. * Currently in classroom use in Europe. * Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.
Author |
: Sadrilla Abdullaev |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 422 |
Release |
: 2013-11-19 |
ISBN-10 |
: 9783319018904 |
ISBN-13 |
: 3319018906 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Magnetic Stochasticity in Magnetically Confined Fusion Plasmas by : Sadrilla Abdullaev
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 |
: Karl-Heinz Spatschek |
Publisher |
: John Wiley & Sons |
Total Pages |
: 642 |
Release |
: 2013-11-12 |
ISBN-10 |
: 9783527638130 |
ISBN-13 |
: 352763813X |
Rating |
: 4/5 (30 Downloads) |
Synopsis High Temperature Plasmas by : Karl-Heinz Spatschek
Filling the gap for a treatment of the subject as an advanced course in theoretical physics with a huge potential for future applications, this monograph discusses aspects of these applications and provides theoretical methods and tools for their investigation. Throughout this coherent and up-to-date work the main emphasis is on classical plasmas at high-temperatures, drawing on the experienced author's specialist background. As such, it covers the key areas of magnetic fusion plasma, laser-plasma-interaction and astrophysical plasmas, while also including nonlinear waves and phenomena. For master and PhD students as well as researchers interested in the theoretical foundations of plasma models.
Author |
: Stephen Lynch |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 512 |
Release |
: 2009-12-23 |
ISBN-10 |
: 9780817646059 |
ISBN-13 |
: 0817646051 |
Rating |
: 4/5 (59 Downloads) |
Synopsis Dynamical Systems with Applications using MapleTM by : Stephen Lynch
Excellent reviews of the first edition (Mathematical Reviews, SIAM, Reviews, UK Nonlinear News, The Maple Reporter) New edition has been thoroughly updated and expanded to include more applications, examples, and exercises, all with solutions Two new chapters on neural networks and simulation have also been added Wide variety of topics covered with applications to many fields, including mechanical systems, chemical kinetics, economics, population dynamics, nonlinear optics, and materials science Accessible to a broad, interdisciplinary audience of readers with a general mathematical background, including senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering A hands-on approach is used with Maple as a pedagogical tool throughout; Maple worksheet files are listed at the end of each chapter, and along with commands, programs, and output may be viewed in color at the author’s website with additional applications and further links of interest at Maplesoft’s Application Center
Author |
: Stephen Lynch |
Publisher |
: Springer |
Total Pages |
: 668 |
Release |
: 2018-10-09 |
ISBN-10 |
: 9783319781457 |
ISBN-13 |
: 3319781456 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Dynamical Systems with Applications using Python by : Stephen Lynch
This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams. After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students’ programming abilities and Python-based exam questions. This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential.