TY - BOOK
AU - Efstathiou,Konstantinos
ED - SpringerLink (Online service)
TI - Metamorphoses of Hamiltonian Systems with Symmetries
T2 - Lecture Notes in Mathematics,
SN - 9783540315506
AV - QC19.2-20.85
U1 - 530.1 23
PY - 2005///
CY - Berlin, Heidelberg
PB - Springer Berlin Heidelberg, Imprint: Springer
KW - Differentiable dynamical systems
KW - Topological Groups
KW - Statistical physics
KW - Theoretical, Mathematical and Computational Physics
KW - Complex Systems
KW - Dynamical Systems and Ergodic Theory
KW - Topological Groups, Lie Groups
KW - Statistical Physics and Dynamical Systems
N1 - Introduction -- Four Hamiltonian Systems -- Small Vibrations of Tetrahedral Molecules -- The Hydrogen Atom in Crossed Fields -- Quadratic Spherical Pendula -- Fractional Monodromy in the 1: - 2 Resonance System -- The Tetrahedral Group -- Local Properties of Equilibria -- References -- Index
N2 - 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
UR - https://doi.org/10.1007/b105138
ER -