Hardcover ISBN:  9780821803752 
Product Code:  MMONO/176 
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eBook ISBN:  9781470445911 
Product Code:  MMONO/176.E 
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AMS Member Price:  $124.00 
Hardcover ISBN:  9780821803752 
eBook: ISBN:  9781470445911 
Product Code:  MMONO/176.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 
Hardcover ISBN:  9780821803752 
Product Code:  MMONO/176 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445911 
Product Code:  MMONO/176.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821803752 
eBook ISBN:  9781470445911 
Product Code:  MMONO/176.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 176; 1998; 177 ppMSC: Primary 58; 70
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.
ReadershipGraduate students and research mathematicians working in the dynamics of Hamiltonian systems; also useful for those studying the geometric structure of symplectic manifolds.

Table of Contents

Chapters

General results of the theory of Hamiltonian systems

Linear theory and classification of singular orbits

IHVF and Poisson actions of Morse type

Centercenter type singular points of PA and elliptic singular points of IHVF

Saddlecenter type singular points

Saddle type singular points

Saddlefocus 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


Reviews

The main goal of the book is to obtain isoenergetic equivalence of IHVFs in some special neighborhoods of a simple singular point. Therefore, in the following chapters, the authors consider each possible type of singular point separately: elliptic, saddlecenter, saddle and focussaddle. Various examples of each case are presented in the last chapter. The interest of the book is that it concentrates on topological aspects of the subject rather than using an analytic point of view. In contrast to most of the books published previously, dynamical properties of the Poisson action are consistently used in order to achieve the results. This 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.
Mathematical Reviews


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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.
Graduate students and research mathematicians working in the dynamics of Hamiltonian systems; also useful for those studying the geometric structure of symplectic manifolds.

Chapters

General results of the theory of Hamiltonian systems

Linear theory and classification of singular orbits

IHVF and Poisson actions of Morse type

Centercenter type singular points of PA and elliptic singular points of IHVF

Saddlecenter type singular points

Saddle type singular points

Saddlefocus 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

The main goal of the book is to obtain isoenergetic equivalence of IHVFs in some special neighborhoods of a simple singular point. Therefore, in the following chapters, the authors consider each possible type of singular point separately: elliptic, saddlecenter, saddle and focussaddle. Various examples of each case are presented in the last chapter. The interest of the book is that it concentrates on topological aspects of the subject rather than using an analytic point of view. In contrast to most of the books published previously, dynamical properties of the Poisson action are consistently used in order to achieve the results. This 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.
Mathematical Reviews