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  • © 2005

Metamorphoses of Hamiltonian Systems with Symmetries

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1864)

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Table of contents (8 chapters)

  1. Front Matter

    Pages N2-IX
  2. Introduction

    • Konstantinos Efstathiou
    Pages 1-8
  3. 1. Four Hamiltonian Systems

    • Konstantinos Efstathiou
    Pages 9-33
  4. 2. Small Vibrations of Tetrahedral Molecules

    • Konstantinos Efstathiou
    Pages 35-58
  5. 3. The Hydrogen Atom in Crossed Fields

    • Konstantinos Efstathiou
    Pages 59-85
  6. 4. Quadratic Spherical Pendula

    • Konstantinos Efstathiou
    Pages 87-111
  7. 5. Fractional Monodromy in the 1: -2 Resonance System

    • Konstantinos Efstathiou
    Pages 113-127
  8. Appendix

    • Konstantinos Efstathiou
    Pages 129-138
  9. References and Index

    • Konstantinos Efstathiou
    Pages 139-145
  10. Back Matter

    Pages 147-150

About this book

Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.

Keywords

  • Hamiltonian
  • Hamiltonian mechanics
  • Mathematica
  • Vibration
  • atom
  • bifurcation
  • bifurcations
  • classical mechanics
  • hydrogen atom
  • integrable systems
  • mechanics
  • monodromy
  • qualitative changes
  • relative equilibria
  • system

Reviews

From the reviews of the first edition:

"This is a well-written book which utilizes modern methods of classical mechanics in the study of four physical Hamiltonian systems with symmetries … . Two appendices are included for completeness. … This book is likely to appeal to specialists in the area." (F. M. Mahomed, Zentralblatt MATH, Vol. 1069, 2005)

Bibliographic Information

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions