© 2006

Construction of Mappings for Hamiltonian Systems and Their Applications

  • Unique description of the mathematical physics of Hamiltonian systems and their application to plasma physics, chaos, dynamical systems, and electromagnetism


Part of the Lecture Notes in Physics book series (LNP, volume 691)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Sadrilla S. Abdullaev
    Pages 1-19
  3. Sadrilla S. Abdullaev
    Pages 21-37
  4. Sadrilla S. Abdullaev
    Pages 39-51
  5. Sadrilla S. Abdullaev
    Pages 83-104
  6. Sadrilla S. Abdullaev
    Pages 105-138
  7. Sadrilla S. Abdullaev
    Pages 139-174
  8. Sadrilla S. Abdullaev
    Pages 197-218
  9. Sadrilla S. Abdullaev
    Pages 219-254
  10. Sadrilla S. Abdullaev
    Pages 255-273
  11. Sadrilla S. Abdullaev
    Pages 299-316
  12. Back Matter
    Pages 317-378

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.


Chaotic behaviour Hamiltonian systems Magnetic field lines Plasma Symplectic maps chaos theory dynamics mechanics physics tokamak transport

Authors and affiliations

  1. 1.Institut für Plasmaphysik Forschungszentrum Jülich GmbHJülichGermany

Bibliographic information

Industry Sectors
IT & Software


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)