Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects)
L. M. Lerman, Ya. L. Umanskiy.
Providence, R.I. : American Mathematical Society, ©1998.
xii, 177 págs. : ilustraciones ; 26 cm.
Serie: Translations of mathematical monographs, ISSN 0065-3282 ; v. 176
ISBN: 0821803751
"Translated from the original Russian manuscript by A. Kononenko and A. Semenovich."
The book can be used by graduate students and researchers interested in studying dynamics of Hamiltonian systems. It can also be useful for people studying the geometric structure of symplectic manifolds.
Resumen: The main topic of this book is the isoenergetic structure of the Liouville foliation generated by an integrable system with two degrees of freedom and the topological structure of the corresponding Poisson action of the group ${\mathbb R}2$. This is a first step towards understanding the global dynamics of Hamiltonian systems and applying perturbation methods. The main attention is paid to the topology of this foliation rather than to analytic representation. In contrast to books published before the authors consistently use the dynamical properties of the action to achieve their results.
Incluye referencias bibliográficas (p. 175-177).
Reseña: MathSciNet, 99b:58115
Contenido
- 1. General results of the theory of Hamiltonian systems
- 2. Linear theory and classification of singular orbits
- 3. IHVF and Poisson actions of Morse type
- 4. Center-center type singular points of PA and elliptic singular points of IHVF
- 5. Saddle-center type singular points
- 6. Saddle type singular points
- 7. Saddle-focus type singular points
- 8. Realization.
