Metamorphoses of Hamiltonian Systems with Symmetries
Efstathiou, Konstantinos.
Metamorphoses of Hamiltonian Systems with Symmetries [electronic resource] / by Konstantinos Efstathiou. - IX, 149 p. online resource. - Lecture Notes in Mathematics, 1864 0075-8434 ; . - Lecture Notes in Mathematics, 1864 .
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.
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.
9783540315506
10.1007/b105138 doi
Differentiable dynamical systems.
Topological Groups.
Statistical physics.
Theoretical, Mathematical and Computational Physics.
Complex Systems.
Dynamical Systems and Ergodic Theory.
Topological Groups, Lie Groups.
Statistical Physics and Dynamical Systems.
QC19.2-20.85
530.1
Metamorphoses of Hamiltonian Systems with Symmetries [electronic resource] / by Konstantinos Efstathiou. - IX, 149 p. online resource. - Lecture Notes in Mathematics, 1864 0075-8434 ; . - Lecture Notes in Mathematics, 1864 .
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.
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.
9783540315506
10.1007/b105138 doi
Differentiable dynamical systems.
Topological Groups.
Statistical physics.
Theoretical, Mathematical and Computational Physics.
Complex Systems.
Dynamical Systems and Ergodic Theory.
Topological Groups, Lie Groups.
Statistical Physics and Dynamical Systems.
QC19.2-20.85
530.1