Metamorphoses of Hamiltonian Systems with Symmetries

Konstantinos Efstathiou (auth.)354024316X, 9783540243168

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.

Table of contents :
Introduction….Pages 1-8
1. Four Hamiltonian Systems….Pages 9-33
2. Small Vibrations of Tetrahedral Molecules….Pages 35-58
3. The Hydrogen Atom in Crossed Fields….Pages 59-85
4. Quadratic Spherical Pendula….Pages 87-111
5. Fractional Monodromy in the 1: -2 Resonance System….Pages 113-127
Appendix….Pages 129-138
References and Index….Pages 139-149