© 2005

Metamorphoses of Hamiltonian Systems with Symmetries

  • Authors

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

Table of contents

  1. Front Matter
    Pages N2-IX
  2. Konstantinos Efstathiou
    Pages 1-8
  3. Konstantinos Efstathiou
    Pages 9-33
  4. Konstantinos Efstathiou
    Pages 35-58
  5. Konstantinos Efstathiou
    Pages 59-85
  6. Konstantinos Efstathiou
    Pages 87-111
  7. Konstantinos Efstathiou
    Pages 113-127
  8. Konstantinos Efstathiou
    Pages 129-138
  9. 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.


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

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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)