Metamorphoses of Hamiltonian Systems with Symmetries
Springer Berlin (Verlag)
978-3-540-24316-8 (ISBN)
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.
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.
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)
| Erscheint lt. Verlag | 11.2.2005 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | IX, 149 p. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 250 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik | |
| Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika | |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| Schlagworte | 70E40, 70H33, 70H05, 70H06, 70K45, 70K75 • Atom • Bifurcation • Bifurcations • classical mechanics • hamiltonian • hamiltonian mechanics • Hamiltonsches System • hydrogen atom • Integrable Systems • Mathematica • Mechanics • Monodromy • qualitative changes • relative equilibria • System • Vibration |
| ISBN-10 | 3-540-24316-X / 354024316X |
| ISBN-13 | 978-3-540-24316-8 / 9783540243168 |
| Zustand | Neuware |
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