Hardcover ISBN:  9780821841051 
Product Code:  ADVSOV/6 
345 pp 
List Price:  $229.00 
MAA Member Price:  $206.10 
AMS Member Price:  $183.20 
Electronic ISBN:  9781470445539 
Product Code:  ADVSOV/6.E 
345 pp 
List Price:  $229.00 
MAA Member Price:  $206.10 
AMS Member Price:  $183.20 

Book DetailsAdvances in Soviet MathematicsVolume: 6; 1991MSC: Primary 53; 57; 58; 70;
In recent years, researchers have found new topological invariants of integrable Hamiltonian systems of differential equations and have constructed a theory for their topological classification. Each paper in this important collection describes one of the “building blocks” of the theory, and several of the works are devoted to applications to specific physical equations. In particular, this collection covers the new topological invariants of integrable equations, the new topological obstructions to integrability, a new Morsetype theory of Bott integrals, and classification of bifurcations of the Liouville tori in integrable systems.
The papers collected here grew out of the research seminar “Contemporary Geometrical Methods” at Moscow University, under the guidance of A. T. Fomenko, V. V. Trofimov, and A. V. Bolsinov. Bringing together contributions by some of the experts in this area, this collection is the first publication to treat this theory in a comprehensive way. 
Table of Contents

Articles

A. Fomenko  The theory of invariants of multidimensional integrable Hamiltonian systems (with arbitrary many degrees of freedom). Molecular table of all integrable systems with two degrees of freedom

G. Okuneva  Integrable Hamiltonian systems in analytic dynamics and mathematical physics

A. Oshemkov  Fomenko invariants for the main integrable cases of the rigid body motion equations

A. Bolsinov  Methods of calculation of the FomenkoZieschang invariant

L. Polyakova  Topological invariants for some algebraic analogs of the Toda lattice

E. Selivanova  Topological classification of integrable Bott geodesic flows on the twodimensional torus

T. Nguyen  On the complexity of integrable Hamiltonian systems on threedimensional isoenergy submanifolds

V. Trofimov  Symplectic connections and MaslovArnold characteristic classes

A. Fomenko and T. Nguyen  Topological classification of integrable nondegenerate Hamiltonians on the isoenergy threedimensional sphere

V. Kalashnikov, Jr.  Description of the structure of Fomenko invariants on the boundary and inside $Q$domains, estimates of their number on the lower boundary for the manifolds $S^3$, $\Bbb R P^3$, $S^1\times S^2$, and $T^3$

A. Fomenko  Theory of rough classification of integrable nondegenerate Hamiltonian differential equations on fourdimensional manifolds. Application to classical mechanics


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In recent years, researchers have found new topological invariants of integrable Hamiltonian systems of differential equations and have constructed a theory for their topological classification. Each paper in this important collection describes one of the “building blocks” of the theory, and several of the works are devoted to applications to specific physical equations. In particular, this collection covers the new topological invariants of integrable equations, the new topological obstructions to integrability, a new Morsetype theory of Bott integrals, and classification of bifurcations of the Liouville tori in integrable systems.
The papers collected here grew out of the research seminar “Contemporary Geometrical Methods” at Moscow University, under the guidance of A. T. Fomenko, V. V. Trofimov, and A. V. Bolsinov. Bringing together contributions by some of the experts in this area, this collection is the first publication to treat this theory in a comprehensive way.

Articles

A. Fomenko  The theory of invariants of multidimensional integrable Hamiltonian systems (with arbitrary many degrees of freedom). Molecular table of all integrable systems with two degrees of freedom

G. Okuneva  Integrable Hamiltonian systems in analytic dynamics and mathematical physics

A. Oshemkov  Fomenko invariants for the main integrable cases of the rigid body motion equations

A. Bolsinov  Methods of calculation of the FomenkoZieschang invariant

L. Polyakova  Topological invariants for some algebraic analogs of the Toda lattice

E. Selivanova  Topological classification of integrable Bott geodesic flows on the twodimensional torus

T. Nguyen  On the complexity of integrable Hamiltonian systems on threedimensional isoenergy submanifolds

V. Trofimov  Symplectic connections and MaslovArnold characteristic classes

A. Fomenko and T. Nguyen  Topological classification of integrable nondegenerate Hamiltonians on the isoenergy threedimensional sphere

V. Kalashnikov, Jr.  Description of the structure of Fomenko invariants on the boundary and inside $Q$domains, estimates of their number on the lower boundary for the manifolds $S^3$, $\Bbb R P^3$, $S^1\times S^2$, and $T^3$

A. Fomenko  Theory of rough classification of integrable nondegenerate Hamiltonian differential equations on fourdimensional manifolds. Application to classical mechanics