Construction of mappings for Hamiltonian systems and their applications
 Author/Creator
 Abdullaev, S. S. (Sadrilla S.), 1951
 Language
 English.
 Imprint
 Berlin ; New York : Springer, c2006.
 Physical description
 xiv, 378 p. : ill. (some col.) ; 24 cm.
 Series
 Lecture notes in physics 691.
Access
Available online
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 www.myilibrary.com MyiLibrary
 www.springerlink.com SpringerLink
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QC20.7 .H35 A24 2006

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QC20.7 .H35 A24 2006
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. [359]376).
 Contents

 Basics of Hamiltonian Mechanics. Perturbation Theory for Nearly Integrable Systems. Mappings for Perturbed Systems. Method of Canonical Transformation for Constructing Mappings. Mappings near Separatrix. Theory. Mappings near Separatrix. Examples. The KAM theory. Chaos. Nontwist and nonsmooth Maps. Rescaling Invariance of Hamiltonian Systems near Saddle Points. Chaotic Transport in Stochastic Layers. Magnetic Field Lines in Fusion Plasmas. Mapping of field Lines in Ergodic Divertor Tokamaks. Mappings of Magnetic field Lines in Poloidal Divertor Tokamaks. Miscellaneous. The Second Order Generating Function. Asymptotic Estimations of the Integral K(h) and L(h) Near Separatrix. Proof of Rescaling Invariance of the Equations of Motion. Relation between v and O. Asymptotic Estimation of the Integral Smm, (10.49). Sample Program for Implementing a Mapping Procedure. References. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 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, mathematicallyrigorous 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 nontwist and nonsmooth 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2006
 Responsibility
 Sadrilla S. Abdullaev.
 Series
 Lecture notes in physics, 00758450 ; 691
 Note
 Also available on the World Wide Web.
 ISBN
 3540309152
 9783540309154