Metamorphoses of Hamiltonian Systems with Symmetries

• Main Author: Efstathiou, Konstantinos (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2005.
• Series: Lecture Notes in Mathematics, 1864
• Subjects: Physics.; Topological groups.; Lie groups.; Dynamics.; Ergodic theory.; System theory.; Theoretical, Mathematical and Computational Physics.; Complex Systems.; Dynamical Systems and Ergodic Theory.; Topological Groups, Lie Groups.; Statistical Physics and Dynamical Systems.
• Physical Description: IX, 149 p. online resource.
• ISBN: 9783540315506
• ISSN: 0075-8434 ;

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.