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A. V. Bolsinov

Integrable Hamiltonian Systems: Geometry, Topology, Classification 1st Edition

by A.V. Bolsinov (Author), A.T. Fomenko (Author)

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Hamiltonian Systems: Geometry, Topology, Classification offers a unique opportunity to explore important, previously unpublished results and acquire generally applicable techniques and tools that enable you to work with a broad class of integrable systems.

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ISBN-10

0415298059
ISBN-13

978-0415298056
Edition

1st
Publisher

CRC Press
Publication date

February 25, 2004
Language

English
Dimensions

6.42 x 1.74 x 9.52 inches
Print length

746 pages

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Editorial Reviews

Review

"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

About the Author

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

Product details

Publisher ‏ : ‎ CRC Press
Publication date ‏ : ‎ February 25, 2004
Edition ‏ : ‎ 1st
Language ‏ : ‎ English
Print length ‏ : ‎ 746 pages
ISBN-10 ‏ : ‎ 0415298059
ISBN-13 ‏ : ‎ 978-0415298056
Item Weight ‏ : ‎ 2.55 pounds
Dimensions ‏ : ‎ 6.42 x 1.74 x 9.52 inches
Best Sellers Rank: #11,955,844 in Books (See Top 100 in Books)
- #483 in Differential Geometry (Books)
- #1,005 in Topology (Books)
- #1,582 in Differential Equations (Books)