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Four-Dimensional Integrable Hamiltonian Systems with Simple Singular Points (Topological Aspects)
About this Title
L. M. Lerman, Research Institute for Applied Mathematics and Cyb, Nizhni Novgorod, Russia and Ya. L. Umanskiy, Total System Services, Inc., Atlanta, GA. Translated by A. Semenovich
Publication: Translations of Mathematical Monographs
Publication Year:
1998; Volume 176
ISBNs: 978-0-8218-0375-2 (print); 978-1-4704-4591-1 (online)
DOI: https://doi.org/10.1090/mmono/176
MathSciNet review: MR1619187
MSC: Primary 58F07; Secondary 58F05, 70H05
ReadershipTable of Contents
Front/Back Matter
Chapters
- General results of the theory of Hamiltonian systems
- Linear theory and classification of singular orbits
- IHVF and Poisson actions of Morse type
- Center-center type singular points of PA and elliptic singular points of IHVF
- Saddle-center type singular points
- Saddle type singular points
- Saddle-focus type singular points
- Realization
- Normal forms of quadratic Hamilton functions and their centralizers in $sp(4,\mathbb {R})$
- The gradient system on $M$ compatible with the Hamiltonian