Lecture Notes in Physics

Construction of Mappings for Hamiltonian Systems and Their Applications

Authors: Abdullaev, Sadrilla S.

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About this book

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.

Reviews

From the reviews:

"The aim of this book is to introduce the reader into the modern theory of Hamiltonian mappings. The book starts by describing the classical methods and theorems such as Jacobi’s Theorem, action variables etc. After, the classical perturbation theory is explained. Many results are illustrated on concrete examples form physics and mechanics. The basic elements of KAM theory are explained for both smooth and non-smooth mappings. This makes the book a valuable source for specialists working with applications of discrete maps." (Alexei Tsygvintsev, Zentralblatt MATH, Vol. 1106 (8), 2007)


Table of contents (13 chapters)

Table of contents (13 chapters)
  • Basics of Hamiltonian Mechanics

    Pages 1-19

    Abdullaev, Sadrilla S.

  • Perturbation Theory for Nearly Integrable Systems

    Pages 21-37

    Abdullaev, Sadrilla S.

  • Mappings for Perturbed Systems

    Pages 39-51

    Abdullaev, Sadrilla S.

  • Method of Canonical Transformation for Constructing Mappings

    Pages 53-81

    Abdullaev, Sadrilla S.

  • Mappings Near Separatrix. Theory

    Pages 83-104

    Abdullaev, Sadrilla S.

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-540-33417-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA in USD
Softcover $99.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Construction of Mappings for Hamiltonian Systems and Their Applications
Authors
Series Title
Lecture Notes in Physics
Series Volume
691
Copyright
2006
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-33417-0
DOI
10.1007/b11554707
Hardcover ISBN
978-3-540-30915-4
Softcover ISBN
978-3-642-06812-6
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XIV, 379
Topics