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9780821803752

Four-Dimensional Integrable Hamiltonian Systems With Critical Points

by Lerman, Lev M.; Umanskiy, Ya. L.
  • ISBN13:

    9780821803752

  • ISBN10:

    0821803751

  • Format: Hardcover
  • Copyright: 1997-12-01
  • Publisher: Amer Mathematical Society

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Summary

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 R2. 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.

Table of Contents

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
Table of Contents provided by Publisher. All Rights Reserved.

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