Integrable Hamiltonian Systems

Geometry, Topology, Classification

A.V. Bolsinov, A.T. Fomenko

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English

CRC Press
25 February 2004

Geometry; Analytic topology

Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and

the general theory underlying their qualitative properties,

singularites, and topological invariants.

The authors, both of whom have contributed significantly to the field, develop

the classification theory for integrable systems with two degrees of freedom. This theory allows one to distinguish such systems up to two natural equivalence relations: the equivalence of the associated foliation into Liouville tori and the usual orbital equaivalence. The authors show that in both

cases, one can find complete sets of invariants that give the solution of the classification problem. The first part of

the book systematically presents the general construction of these invariants, including many examples and applications. In the second part, the authors apply the general methods of the classification theory to the classical integrable problems in rigid body dynamics and describe their topological portraits, bifurcations of Liouville tori, and local and global topological invariants. They show how the classification theory helps find hidden isomorphisms between integrable systems and present as an example their proof that two famous systems--the Euler case in rigid body dynamics and the Jacobi problem of geodesics on the ellipsoid--are orbitally equivalent.

Integrable Hamiltonian Systems: Geometry, Topology, Classification offers a unique opportunity to explore important, previously unpublished results and acquire generally applicable techniques and tools that enable you to work with a broad class of integrable systems.

By: A.V. Bolsinov, A.T. Fomenko
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 234mm, Width: 156mm, Spine: 44mm
Weight: 1.161kg
ISBN: 9780415298056
ISBN 10: 0415298059
Pages: 746
Publication Date: 25 February 2004
Audience: College/higher education , General/trade , Professional & Vocational , Primary , ELT Advanced
Format: Hardback
Publisher's Status: Active

Bolsinov, A.V.; Fomenko, A.T.

Reviews for Integrable Hamiltonian Systems: Geometry, Topology, Classification

This book provides an introduction to the problem of classification of integrable Hamiltonian systems. It presents, in a systematic way, a great deal of material previously available only in journals. - Zentralblatt MATH, 1056