Overview

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 equation. In particular, this collection covers the new topological obstructions to integrability, a new Morse-type theory of Bott integrals, and classification of bifurcations of the Liouville tori in integral 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.

Full Product Details

Author:   A. T. Fomenko
Publisher:   American Mathematical Society
Imprint:   American Mathematical Society
Volume:   No. 6
Weight:   0.850kg
ISBN:  

9780821841051

ISBN 10:   082184105
Pages:   345
Publication Date:   01 December 1991
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   To order  
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Table of Contents

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 by A. T. Fomenko Integrable Hamiltonian systems in analytic dynamics and mathematical physics by G. G. Okuneva Fomenko invariants for the main integrable cases of the rigid body motion equations by A. A. Oshemkov Methods of calculation of the Fomenko-Zieschang invariant by A. V. Bolsinov Topological invariants for some algebraic analogs of the Toda lattice by L. S. Polyakova Topological classification of integrable Bott geodesic flows on the two-dimensional torus by E. N. Selivanova On the complexity of integrable Hamiltonian systems on three-dimensional isoenergy submanifolds by T. Z. Nguyen Symplectic connections and Maslov-Arnold characteristic classes by V. V. Trofimov Topological classification of integrable nondegenerate Hamiltonians on the isoenergy three-dimensional sphere by A. T. Fomenko and T. Z. Nguyen 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 $T^3$ by V. V. Kalashnikov, Jr. Theory of rough classification of integrable nondegenerate Hamiltonian differential equations on four-dimensional manifolds. Application to classical mechanics by A. T. Fomenko.

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