Four-dimensional Integrable Hamiltonian Systems With Simple Singular Points (topological Aspects) (translations Of Mathematical Monographs)

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. Emphasis is placed on the topology of this foliation rather than on analytic representation. In contrast to previously published works in this area, here the authors consistently use the dynamical properties of the action to achieve their results. 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 Bibliography. Contains the topic of 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 book emphasises on the topology of this foliation rather than on analytic representation.